ELEMENTS  OF 

MECHANICAL   DRAWING 


THEIR  APPLICATION  AND 


A  COURSE  IN  MECHANICAL  DRAWING 
FOR  ENGINEERING  STUDENTS. 


BY 


ALPHA  PIERCE  JAMISON,  M.E., 

Assistant  Professor  of  Mtckanicul  Drawing  in  Purdue. 


FIRST    EDITION, 
FIRST    THOUSAND. 


NEW  YORK: 
JOHN   WILEY    &    SONS. 

LONDON:   CHAPMAN    &    HALL,  LIMITED. 
1904. 


I 

Copyright,  1904, 

BY 
A.  P.  JAMISON. 


ROBERT  DRUMMOND,   PRINTER,   NBW  YORK. 


PREFACE. 


HAVING  in  charge  the  instruction  of  the  Freshman  Class, 
Purdue  University,  in  the  subject,  the  writer  has  compiled  the 
accompanying  notes  on  Mechanical  Drawing  to  facilitate  the 
work  of  administration. 

The  intent,  throughout,  has  been  to  prepare  a  work  embracing 
those  branches  of  the  subject  necessary  to  give  the  student  such 
knowledge  as  will  prepare  him  to  pursue  a  course  in  Engineering, 
and  such  practice  in  drawing  as  will  qualify  him  to  do  ordinary 
commercial  draughting. 

The  work  is  arranged  for  students  having  a  knowledge  of 
plane  geometry  such  as  is  offered  in  the  High  Schools,  Prepara- 
tory Schools,  and  Colleges. 

Acknowledgment  is  made  of  many  valuable  suggestions  and 
criticisms  offered  by  Professors  M.  J.  and  Katherine  E.  Golden, 
and  by  Messrs.  R.  B.  Trueblood  and  A.  M.  Wilson,  co-laborers 
in  the  work  of  administration. 

A.  P.  JAMISON 

LAFAYETTE,  IND.,  March,  1904. 

ill 


Llti 


CONTENTS. 

PART   I. 

CHAPTER  I. 
ELEMENTARY  PRINCIPLES  AND  DEFINITIONS. 

SECTION  PACE 

1.  Drawing I 

2.  Drawing  of  Objects  as  they  Appear I 

3.  Drawing  of  Objects  as  they  Exist i 

4.  Detail  Drawing 3 

5.  Assembled  Drawing 3 

6.  The  Divisions  of  Drawing 3 

7.  Shop  Drawing 3 

8.  Show  Drawing 3 

9.  Relation  of  the  Lines  of  an  Object 3 

10.  Relation  of  the  Faces  of  an  Object 4 

it.  Choosing  the  Front  Face 5 

12.  Relation  of  Lines  and  Faces  Shown  by  a  Complete  Mechanical  Drawing 

of  a  Cube   5 

13.  Arrangement  of  the  Drawing 6 

14.  Definition  of  Mechanical  Drawing 6 

15.  Naming  the  Faces  of  an  Object 6 

16.  Elevations 8 

17.  Plan  and  Bottom 8 

18.  Sections 8 

19.  Longitudinal  Section 8 

20.  Transverse  Section 8 

21.  Angular  Section 9 

22.  Full  Section 9 

23.  Half  Section 9 

24.  Detail  Section 9 

25.  Explanatory  of  Sections 9 

26.  Drawing  Sections n 

27.  Arrangement  of  Sections  on  the  Drawing II 

28.  Cross-hatching n 

v 


vi  CONTENTS. 


29.  Lines 12 

30.  Lines  of  the  Drawing 12 

31.  Border  Lines 12 

32.  Center  Lines 12 

33.  Section  Lines 13 

34.  Construction  Lines 14 

35.  Projection  Lines 14 

36.  Dimension  Lines 14 

37.  Guide  Lines 14 

38.  Light  and  Shade 14 

39.  Line  Shading 14 

40.  Shade  or  Shadow  Lining 14 

41.  Drawing  to  Scale 16 

42.  Choosing  the  Scale 16 

43    Balance  and  Symmetry  of  a  Drawing 18 

44.  Flexibility  of  the  Drawing 19 

45.  Dimensioning 20 

46.  Selection  of  the  Necessary  Views 21 

47.  Usual  Number  of  Views. 22 

48.  Use  of  Dashed  and  Dotted  Lines  to  Reduce  the  Number  of  Views 22 

49.  Beginning  to  Draw 22 

50.  Drafting-room  Practice '. 23 

51.  The  Time  Element  in  Drawing 24 

52.  Conventions 25 

CHAPTER  II. 
LETTERS,  FIGURES,  AND  LETTERING. 

53.  Fundamentals 26 

54.  A  Study  of  Letters 28 

55.  Modifications 32 

56.  Suggestions 34 

57.  Combinations  and  Spacings. 34 

58.  Figures 34 

59.  Fractions 36 

60.  Lower-case  Alphabet 36 

61.  Mechanical  Letters 37 

CHAPTER  IIL 
PROJECTION. 

62.  Scenographic  Projection 39 

63.  Orthographic  Projection. 39 

64.  The  Planes  of  Projection 40 

65.  The  Four  Quadrants 40 


CONTENTS.  vii 

SECTION  PAGE- 

66.  The  Projection  of  a  Point,  with  the  Planes  V  and  H  at  Right  Angles 42 

67.  The  Planes  V  and  H  Revolved. 43 

68.  The  Conventional  Projection  of  a  Point 43 

69.  The  Conventional  Assumption  of  a  Point 44 

70.  The  Projection  of  Any  Straight  Line 45 

71.  The  Projection  of  a  Line  which  is  Parallel  to  one  of  the  Planes  of  Pro- 

jection    45 

72.  To  Find  the  True  Length  of  a  Line 46 

73.  The  Projection  of  a  Straight  Line  which  is  Perpendicular  to  One  of  the 

Planes  of  Projection , 48 

74.  The  Assumption  of  a  Plane 48 

75.  To  Draw  the  Projections  of  a  Hollow  Cube 49 

76.  To  Draw  th    P  ejections  of  a  Hexagonal  Nut. 51 

77.  The  Projections  of  a  Small  Hand-wheel 54 

78.  Projections  of  the  Frustum  of  a  Pyramid 57 

79.  Projections  of  the  Frustum  of  a  Cone 62 

80.  The  Intersection  of  Two  Cylinders  at  Right  Angles 63 

81.  The  Intersection  of  a  Cone  and  Cylinder 67 

82.  The  Intersection  of  Two  Cylinders  at  an  Angle  of  45°. 70 

83.  A  Practical  Development 71 

84.  First  and  Third  Quadrant  Projections 73 

85.  Isometric  Projection 74 

To  Dimension  an  Isometric  Drawing 78 

Isometric  Scales 78 

86.  Elementary  Examples 80 


CHAPTER  IV. 
DRAWING  TOOLS  AND  MATERIALS. 

87.  Introductory 83 

88.  The  Ruling-pen 85 

89.  The  Compass 91 

90.  The  Dividers 93 

91.  The  Bow-pen 94 

92.  The  Bow-pencil 95 

93.  The  Bow-dividers 96 

94.  The  Box  for  Leads 96 

95.  The  Care  of  Instruments 96 

96.  Drawing-boards 96 

97.  The  T-Square 97 

98.  The  Triangles 98 

99.  Irregular  Curves 100 

100.  The  Architect's  Scale 100 

101.  Thumb-tacks 103 


viii  CONTENTS. 

SECTION  PAGE 

102.  Pencils  and  Leads , 104 

103.  Pens  and  Pen-holders 106 

104.  Erasers 107 

105.  Ink 107 

106.  Rag  and  Blotter 108 

107.  Horn  Centers 108 

108.  Section  Liners 108 

109.  Erasing-shields 109 

1 10.  Protractors 109 

in.  Scale-guard , 109 

112.  Proportional  Dividers 109 

113.  Erasing-knives 109 

114.  Soap-stone  Pencil 109 

115.  Paper 109 

1 16.  To  Make  an  Erasure  on  Paper in 

117.  Profile  and  Cross-section  Paper 112 

118.  Tracing-paper 112 

119.  Blue-print  Paper 112 

120.  Tracing-cloth 113 

121.  To  Make  an  Erasure  on  Tracing-cloth 113 


CHAPTER  V. 
THE  REPRODUCTION  OF  DRAWINGS. 

122.  Introductory 115 

123.  Blue-printing 116 

124.  Exposure 117 

125.  Washing 1 18 

126.  Drying 1 18 

127.  Photography 119 

128.  The  Hectograph 119 

129.  The  Mimeograph 119 


CHAPTER  VI. 
PATENT-OFFICE  DRAWINGS. 

130.  Introductory 120 

131.  Drawings 120 

132.  Requisites  of  Drawings 120 

133    Three  Editions  of  Drawings 120 

134.  Uniform  Standard 121 

135.  Paper  and  Ink. 121 


CONTENTS.  ix 

SECTION  PAGE 

136.  Size  of  Sheet  and  Marginal  Lines 121 

137.  Character  and  Color  of  Lines 121 

138.  Few  Lines  and  Little  or  no  Shading 121 

139.  Scale  of  the  Drawing 122 

140.  Letters  of  Reference 122 

141.  Signatures  of  Inventor  and  Witnesses 124 

142.  Title 124 

143.  Large  Views 124 

144.  Figures  for  Gazette 1 24 

145.  Drawings  to  be  Rolled  for  Transmission 124 

146.  No  Stamp,  Advertisement,  or  Address  Permitted  on  the  Face  of  Draw- 

ings   124 

147.  Drawings  for  Designs 125 

148.  Drawings  for  Reissue  Applications 125 

149.  Defective  Drawings 125 

150.  Drawings  Furnished  by  Office 125 


CHAPTER  VII. 
GEARING. 

151.  Introductory 126 

152.  Fundamental  Curves 126 

The  Cycloid 126 

The  Epicycloid 127 

The  Hypocycloid 1 28 

The  Involute 1 29 

153.  Glossary  of  Terms 1 29 

Tooth 129 

Space 129 

Circular  Pitch 129 

Tooth  Face 130 

Tooth  Flank 130 

Front  of  the  Tooth 130 

Back  of  the  Tooth 130 

Pitch  Point 130 

Addendum  Circle 130 

Root  Circle 130 

Clearance 130 

Dedendum  Circle 130 

Depth  of  Tooth !3o 

Fillet 130 

Pitch  Diameter !^o 

Diametral  Pitch 130 

Driver !^o 

Follower. 


X  CONTENTS. 

SECTION  PAGE 

154.  Usual  Proportions  for  Teeth 130 

155.  Development  of  Formulae i  ^i 

156.  Kinds  of  Gears 131 

Spur  gears    132 

Rack I32 

Annual  or  Internal  Gear I32 

157.  Systems  of  Teeth 132 

Cycloidal I32 

Involute 132 

158.  Interchangeability 132 

159.  Methods  of  Drawing  the  Tooth  Outline 132 

Exact  Method 133 

Approximate  Method 133 

160.  Spur-gears.  .  . 133 

Exact,  Non-interchangea'-    ,  Cycloidal 133 

Exact,  Interchangeable,  Cycloidal 134 

Exact  Involute 135 

Approximate  Cycloidal 136 

Approximate  Involute 138 

161.  Rack  and  Pinion 138 

Exact,  Non -interchangeable,  Cycloidal ,    138 

Exact,  Interchangeable,  Cycloidal 141 

Exact  Involute 141 

Approximate  Cycloidal 141 

Approximate  Involute 142 

162.  Internal  Gears 142 

Exact  Cycloidal 142 

Exact  Involute 144 

Approximate  Cycloidal 144 

Approximate  Involute 144 


CHAPTER  VIII. 
COLOR  WORK. 

TINTING. 

163.  Introductory 145 

164.  Outfit 145 

165.  Making  a  Stretch 146 

166.  Mixing  the  Colors 146 

167.  Flat  Wash 147 

168.  Shading 147 

STIPPLING. 

169.  Introductory 149 

170.  Method  of  Procedure 150 


. 

CONTENTS.  XI 


PART  II. 

CHAPTER  IX. 

SKETCHING. 
SECTION  PAGB 

171.  Introductory 152 

172.  Sheet  No      i 152 

173-      "        "      2 J52 

174.      "        "      3 J54 

175-      "        "      4 , 154 

176.  "       "      5 155 

177.  "        "       6  to  20  inclusive 155 

178.  "    *   "     21 157 

179-      "       "    22 157 

iSo.      "        "    23 157 

181.  "       "    24 170 

182.  "       "    25 170 

183.  "       "    26 170 

184.  "       "    27 170 

185.  "       "    28 170 

186.  '«       "    29 170 

187.  "       "    30 170 

188.  "       "    31 170 

189.  "       "    32 170 

190-      "       "    33 171 

191.      "       "    34  to  40  inclusive 171 


CHAPTER  X. 
THE  MECHANICAL  EXECUTION  OF  DRAWINGS. 

192.  Introductory 172 

193.  Sheet  No.  i 172 

194.  "   "   2 176 

195   "   "   3 176 

196.   "   "   4 178 

197-   "   "   5 178 

198.   "   "   6 182 

199-   "   "   7 184 

200.  "   "   8 188 

201.  "   «'   9 188 

202.  "     "   10 190 

203.  "   "  II 192 

204.  "     "   12 192 


xii  CONTENTS. 

SECTION  PAGE 

205.  Sheet  No.  13 196 

206.  "  "  14 196 

207.  "  "  15 198 

208.  "  "  16 200 

209.  "  "   17 200 

210.  "  "   l8 200 

211.  "  "   19 200 

212.  "  "   20 208 

213.  "  "   21 208 

214.  "  "   22 2C8 

215.  "  "   23 21O 

216.  "  "   24 2IO 

217.  "  "   25 210 

218.  '*  "   26 210 

219.  "  "   27 21O 

220.  "  "   28 2l6 

221.  "  "   29 2l8 

222.  "  "   30 220 

223.  "  "   31 222 

224.  "  "    32  to  36  inclusive 225 


TABLES. 

225.  Explanatory 225 

Steam-  and  Gas-pipe 225 

Bolts  and  Nuts 226 

Gear  Teeth 137,  138 


MECHANICAL    DRAWING. 


PART  I. 


CHAPTER  I. 
ELEMENTARY  PRINCIPLES  AND  DEFINITIONS. 

1.  Drawing. — Drawing  is  the.  art  of  putting  one's  impressions 
into  visible  form,  and  may  be  divided  into  two  general  classes: 

(1)  the  drawing  of  objects  viewed  from  a  finite  distance,  and 

(2)  the  drawing  of  objects  viewed  from  an  infinite  distance. 

2.  Drawing  of  Objects   as  they  Appear. — By  the  first  class 
of  drawing  is  meant  the  free-hand  work  of  the  artist,  drawings 
of  things  as  they  appear  to  the  eye,  as  they  impress  one.     In 
such  drawing  there  is  but  one  point  of  sight  * — the  observer's 
eye — and  the  lines  of  sight  f  are  straight  lines  radiating  from 
this  one  point  and  extending  to  the  different  points  of  the  object 
or  objects,   as  the  case  may  be.     (See  Fig.   i.)     Paintings  of 
landscapes,  portraits,  miniatures,  the  sketch-work  of  the  news- 
paper artist,  etc.,  are  examples  of  this  class  of  drawing. 

3.  Drawing  of  Objects  as  they  Exist. — By  the  second   class 
of  drawing  is  meant  the  drawing  of  objects  as  they  actually  exist 
and  not  as.  they  appear  to  the  eye.     Such    drawing  is  called 
"Mechanical  EJrawing,"  and  the  point  of  sight  being  at  an  infinite 
distance,  the  lines  of  sight  are  practically  parallel  and  are  so 

*  The  point  of  sight  is  that  point,  imaginary  or  real,  from  which  an  object  is 
viewed;  we  see  with  two  eyes,  but  only  one  point  of  sight  is  assumed. 

t  A  line  of  sight  is  an  imaginary  straight  line  connecting  any  point  of  the  object 
and  the  point  of  sight. 


MECHANICAL  DRAWING. 


assumed.      Fig.  2  depicts  the  lines  of  sight  for  such  drawing. 
Drawings  of  machinery,  bridges,  masonry  construction,  plans  for 


Lines 


DRAWING 


SHOWING  THE  POINT  OF 
SIGHT  AT  A  FINITE  DISTANCE 


buildings,  etc.,  are  examples  of  this  class  of  drawing,  and  this  is 
the  kind  of  drawing  with  which  engineers  are  concerned. 


OF  SIGHT  AT  AN 
INFINITE  DISTANCE 


FIG.  2 


Mechanical   Drawing   may,   in   turn,   be    divided   into    two 
general  classes:   (i)  detail  drawing  and  (2)  assembled  drawing. 


ELEMENTARY  PRINCIPLES  AND  DEFINITIONS. 


4.  Detail  Drawing. — To  detail  means  to  separate,  to  "tell" 
in  detail;  detail  drawing  means  to  separate  an  object — a  machine, 
for  example — into  its  various  parts  and  to  tell  of  each  by  a  mechani- 
cal drawing  of  it.     Detail  drawings  are  used  for  shop  purposes, 
that  is,  for  "getting  out  '  the  piece — for  its  manufacture. 

5.  Assembled  Drawing. — To  assemble  means  to  collect  into 
one  place  or  body;  assembled  drawing  means  to  collect  the  vari- 
ous parts  of  an  object — a  machine,  again,  for  example — and  to 
draw   it   assembled   as   a   whole.     Assembled   drawings   are   to 
11  picture"   the  object  as  it  will  appear  when  complete.     Such 
drawings  are  mostly  used  for  erection  purposes. 

Detail  and  assembled  drawing  may  be  subdivided  into  two 
other  general  classes:  (i)  shop  drawing  and  (2)  show  drawing, 
presenting  the  subject  "Drawing"  thus: 

6.  The  Divisions  of  Drawing. 

Drawing  of  objects  as  they  appear,  called    Per- 
spective Drawing. 

(The  point  of  sight  at  a  finite  distance.) 


Drawing. 


Mechanical  Drawing. 

(The  point  of  sight  at  an 
infinite  distance.) 


Detail         (  Shop  drawing. 
Drawing.  (  Show  drawing. 

Assembled  (  Shop  drawing. 
Drawing.  (  Show  drawing. 

7.  Shop  Drawing. — A  shop  drawing  is  a  drawing  to  facilitate 
manufacture,  and   may  be  a  detail  or  an  assembled  drawing,  or 
both.    It  is  usually  an  outline  *  drawing,  very  plain  and  free 
from  ornamentation. 

8.  Show  Drawing. —  A  show  drawing  is  a  drawing  calculated 
to  facilitate  the  sale  of  an  article.    It  is  usually  an  ornamented 
drawing,!  and  is  used  for  catalogue  and  "show"  purposes. 

9.  Relation   of  the  Lines  of  an    Object. — Every  line  of  an 
object  bears  a  certain  relation  to  every  other  line  of  the  same 
object,  and  in  a  mechanical  drawing  of  that  object  the  lines  of 

*  An  outline  drawing  is  a  single-line  drawing  of  the  outline  of  an  object, 
t  An  ornamented  drawing  is  a  drawing  beautified  by  the  addition  of  shades 
and  shadows,  colors,  ornamental  lettering,  etc 


4  MECHANICAL  DRAWING. 

the  drawing  must  be  so  arranged  as  to  present  this  relation  to 
the  eye. 

For  example,  consider  a  cube:  all  of  its  edges  are  straight 
lines,  and  are  either  parallel  or  perpendicular  to  one  another; 
therefore,  in  the  mechanical  drawing  of  the  cube  all  of  the  lines 
of  the  drawing  must  be  straight  lines  either  parallel  or  perpen- 
dicular to  one  another;  furthermore,  two  adjacent  edges  of  the 
same  face  are  at  right  angles  to  each  other,  and  opposite  edges 
are  parallel;  hence  in  the  mechanical  drawing  of  that  face  the 
two  adjacent  lines  must  form  a  right  angle  and  opposite  lines 
must  be  parallel.  From  this  it  is  obvious  that  the  mechanical 
drawing  of  any  one  face  of  a  cube  is  a  perfect  square. 

10.  Relation  of  the  Faces  of  an  Object. — To  maintain  the 
relation  of  the  lines  of  an  object  it  is  necessary  that  a  separate 


FIG.  3. 
A  Perspective  Drawing. 

drawing  of  every  face,  or  side,  be  constructed,  for,  in  addition 
to  the  relation  of  the  lines  of  an  object,  the  faces  of  that  object 
bear  a  definite  relation  to  one  another.  To  depict  the  relation 
of  the  faces  of  an  object  they  are  referred  to  one  face  called 
the  " front  face." 


ELEMENTARY  PRINCIPLES  AND  DEFINITIONS.  5 

11.  Choosing  the  Front  Face.— To  represent  these  relations 
on  paper  it  is  necessary  that  the  front  face  be  decided  on.     In 
most  cases  this  is  readily  determined  by  the  objects'   use  and 
natural  position. 

For  example,  consider  the  ordinary  dwelling-house:  it  fronts 
a  certain  way  and  has  a  well-understood  front.  Facing  this  end 
of  the  building,  one  views  the  front  face.  (Fig.  3.)  That  face 
on  the  right  hand  is  called  the  right  face  or  side;  that  on  the  left, 
the  left  face  or  side;  the  face  at  the  rear,  the  rear  face;  etc. 

This  reasoning  applies  to  any  object  as  well  as  to  the  building 
in  question;  but  should  there  be  no  well- defined  front  face,  the 
choosing  of  one  is  optional  with  the  draughtsman. 

12.  Relation   of  Lines   and   Faces   Shown   by   a   Complete 
Mechanical  Drawing  of  a  Cube. — Having  determined  upon  the 
front  face  of  an  object,  construct  a  drawing  representing  all  the 
lines  of  that  face  in  their  true  position  and  relation  with  respect 
to  one  another.     For  a  cube,  as  before  stated,  the  drawing  of 
the  front  face  will  be  a  perfect  square;   likewise,  the  drawing  of  all 
of  the  faces  will  be  perfect  squares.    Now  to  "show"  the  relation 
of  these  various  faces : — 


Top 


Rear 


Lt.Side 


Front 


Rt.Side 


FIQ.  4. 


Bottom 


H  Q 

A   Mechanical  Drawing. 


o  MECHANICAL  DRAWING. 

(Fig.  4.)  Beginning  with  the  front  face,  A-B-C-D,  drawn,  the 
right  face  is  at  the  right  side  of  the  front  face  and  is  tangent  to 
it,  having  the  line  (edge)  B-C  in  common  with  it;  the  left  face  is 
at  the  left  of  the  front  face  and  has  the  line  (edge)  A-D  in  com- 
mon with  it;  the  bottom  is  at  the  bottom  and  is  tangent  along 
the  line  D-C\  the  top  face  is  at  the  top  and  has  the  line  (edge) 
A-B  in  common  with  the  front  face. 

The  rear  face  yet  remains  to  be  provided  for;  this  face  has 
an  edge  in  common  with  the  right  face,  one  with  the  left  face, 
one  with  the  top  and  one  with  the  bottom  face.  The  drawing 
representing  the  rear  face  may  be  placed  tangent  to  any  one  of 
the  drawings  representing  the  above  faces;  the  one  taken  is 
usually  determined  by  the  limits  of  the  paper,  but  is  optional 
with  the  draughtsman. 

13.  Arrangement  of  the  Drawing. — Should  all  drawings  be 
constructed  with  adjacent  sides  tangent  along  common  lines  the 
drawings  would  not  admit  of  the  convenient  addition  of  dimen- 
sion lines,  figures,  and  notes — details  necessary  to  every  drawing; 
also,    such   an   arrangement   would   only   apply   to   rectangular 
figures.   For  the  convenient  application  of  the  foregoing  principles 
the  drawings  are  separated  an  optional  distance  (Fig.   i,  Plate 
No.  i),  those  at  the  sides  of  the  front  face — the  right  and  left 
faces — being  moved  in  a  horizontal  direction  only,   and  those 
at  the  top  and  bottom  moved  in  a  vertical  direction  only. 

It  will  be  observed  that  all  of  the  drawings  are  contained 
between  two  pairs  of  lines,  one  pair  horizontal  and  the  other 
vertical;  should  one  or  more  of  the  drawings  be  "out  of  line" 
with  these  two  pairs  of  lines  the  drawing  would  be  incorrect. 

14.  Definition     of    Mechanical    Drawing. — From    the    fore- 
going, a  mechanical  drawing  of  an  object  may  be  said  to  be  a 
separate  drawing  of  each  face  of  the  object,  and  these  several 
drawings    so  arranged  as  to  bear  the  proper   relation  to  one 
another. 

15.  Naming  the  Drawings. — In  the  explanation  mention  has 
been   made    of   the   different   faces   of   an   object;    the  several 
drawings  representing  these  faces  are  now  to  be  named. 


ELEMENTARY  PRINCIPLES  AND  DEFINITIONS. 
PLATE  No.  i. 


u 


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8  MECHANICAL  DRAWING. 

The  drawing  representing  the  front  face  of  an  object  is  called 
a  front  view  or  front  elevation,  and  drawings  of  the  right  and 
left  faces  are  called  side  views,  right  and  left  elevations  respect- 
ively, or  collectively  side  elevations,  and  the  drawing  representing 
the  rear  face  is  called  the  rear  view  or  rear  elevation. 

1 6.  Elevations. — Elevations    are   views   in   which   all   of  the 
lines  of  sight  are  parallel,  horizontal  lines.     Side  elevations  are 
at  right  angles  to  the  front  and  rear  elevations,  and  vice  versa. 
Elevations  should  always  be  between  the  same  limiting  pair  of 
horizontal  lines.     (Fig.  i,  Plate  No.  i.) 

17.  Plan   and    Bottom. — The   drawing  representing  the  top 
of  an  object  is  called  the  top  view  or  plan,  and  that  of  the  bottom 
is  called  the  bottom  view  or  bottom.     Plan  and  bottom  are  views 
in  which  all  the  lines  of  sight  are  parallel,  vertical  lines. 

Plan  and  bottom  are  at  right  angles  to  elevations,  and  vice 
versa.  Plan  and  bottom  should  always  be  between  the  same 
limiting  pair  of  vertical  lines  with  an  elevation.  The  plan  may 
be  in  line  with  one  elevation,  and  the  bottom  view  in  line  with  a 
different  elevation  and  the  drawing  be  correct,  though  usually 
they  are  in  line  with  each  other  and  with  the  front  elevation. 

A  name  has  now  been  given  the  drawing  of  each  face  of  an 
object,  though  a  plan  and  one  or  two  elevations  are  quite  sufficient 
to  represent  simple,  solid  objects.  To  represent  objects  with 
"interior  features,"  it  is  necessary  to  add  other  views  than  those 
given  above,  views  called  "  sections." 

18.  Sections. — To  section  means  to  separate  by  cutting,  the 
"section"   being   that   portion   cut;    in  mechanical  drawing,   a 
section  is  a  drawing  of  the  cut  portion. 

Sections  may  be  divided  into  three  general  classes:  (i)  longi- 
tudinal sections,  (2)  transverse  sections,  and  (3)  angular  sections. 
These  may  be  divided  into  full,  half,  and  detail  sections. 

19.  Longitudinal   Section. — A  longitudinal  section  is  a  sec- 
tion in  the  direction  of  the  length  of  an  object  and  may  be  hori- 
zontal (cut  on  a  horizontal  plane),  vertical  (cut  on  a  vertical  plane), 
or  angular  (being  cut  on  a  plane  at  some  intermediate  angle) . 

20.  Transverse   Section. — A   transverse   section   is   a   section 


ELEMENTARY  PRINCIPLES  AND  DEFINITIONS.  9 

at  right  angles  to  a  longitudinal  section,  and  may  be  horizontal, 
vertical,  or  angular  according  to  the  position  of  the  plane  on 
which  it  is  cut. 

21.  Angular  Section. — An  angular  section  is  any  other  than 
a  longitudinal  or  transverse  section. 

22.  Full  Section. — A  full  section  is  a  section  made  by  cutting 
entire  and  in  one  plane,  that  is,  by  cutting  in  two. 

23.  Half  Section.     A  half  section  is  a  section  made  by  cut- 
ting in  two  planes  at  right  angles,  that  is,  by  cutting  out  one 
quarter. 

24.  Detail   Section. — A  detail  section  is  any  specially  taken 
section. 

25.  Explanatory  of  Sections. — Plate  No.  2.  Fig.  i  is  a  mechan- 
ical drawing  (plan  and  elevation)  of  a  rectangular  pyramid,  the 
dotted  lines  representing  a  hole  in  it — "  interior  features."     Fig.  2 
is  a  full,  longitudinal  section,  the  drawing  being  a  plan  and  ele- 
vation of  one- half  of  the  pyramid  and  showing  only  visible  lines. 
Fig.  3  is  a  similar  drawing  of  a  half,  longitudinal  section  of  the 
pyramid.     Fig.  4  is  a  plan  and  elevation  of  a  full,  transverse 
section,  and  Fig.  5  a  like  drawing  of  a  half,  transverse  section 
of  the  pyramid.     Fig.  6  is  a  plan  and  elevation  of  a  full,  angular 
section,  the  inclined  line  (A-B)   across  the  elevation  indicating 
the  plane  on  which  the   section   is   taken;    the  view  between 
the  plan  and  the  elevation   is  a   drawing  of  the  cut   portion 
and  is  the  conventional  method  of  representing  such  sections. 
Fig.  7  is  a  left  and  front  elevation  of  a  hollow  tube,  the  lined 
portion  in  the  right  end  of  the  front  elevation  being  a  conven- 
tional   method    of    indicating    a    full,    transverse    section.    The 
lower  portion  of  the  drawing  represents  a  horizontal,  full,  longi- 
tudinal section  and  is  a  front-  and  end-view  drawing.    Fig.  8 
depicts  a  full,  transverse  section,  and  a  full,  detail,  longitudinal 
section   showing  the  manner  in  which  the  two  pieces  are  held 
together.     Fig.  9  is  a  front  and  side  elevation  of  a  small,  three- 
armed  hand- wheel;  the  drawing  at  the  right  being  a  side  eleva- 
tion, sectioned,  and  being  cut  in  two,  is  a  full,  sectional  eleva- 
tion ;  the  left  figure  illustrates  the  use  of  detail  sections.    Fig.  10 


IO 


MECHANICAL  DRAWING. 


PLATE  No.  2. 


ELEMENTARY  PRINCIPLES  AND  DEFINITIONS.  II 

shows  a  half,  sectional  elevation,  and  Fig.  n  another  example 
of  detail  sectioning. 

26.  Drawing  Sections. — In  drawing  sections  it  is  customary 
not  only  to  draw  the  cut  portion,  but  also  all  points  and  lines  that 
are  visible  when  viewing  the  section;    however,  it  is  allowable, 
and  often  quite  convenient,  to  draw  the  cut  portion  only. 

27.  Arrangement  of  Sections  on  the  Drawing. — It  will  have 
been  noted   that   the  plan,   elevations,   and  bottom  view  have 
specially  assigned  positions  on  the  drawing..    The  drawing  of 
sections,  in  so  far  as  possible,  should  be  placed  as  follows:  All 
sections  taken  on  a  horizontal  plane,  conventionally  indicated 
by  a  horizontal  line  (usually  a  horizontal  center  line),  should  be 
placed  either  above  or  below  the  view  sectioned.     All  sections 
taken  on  a  vertical  plane,  conventionally  indicated  by  a  vertical 
line  (usually  a  vertical  center  line),  should  be  placed  either  to 
the  right  or  to  the  left  of  the  view  sectioned.     All  sections  taken 
at  an  angle,  conventionally  indicated  by  a  straight  line  drawn 
through  the  portion  to  be  sectioned,  should  be  placed  at  right 
angles,  either  way,  to  the  line  (plane)  on  which  the  section  is 
taken — the  general  rule  being  to  assume  the  section  as  taken, 
that  is,  the  object  as  having  been  cut  at  the  proper  place,  and 
calling  this  a  front  elevation,  to  draw  a  plan,  bottom,  or  side 
elevation,  as  the  case  may  warrant,  of  the  cut  portion. 

Sections  are  usually  indicated  as  being  cut  portions  by  cer- 
tain conventions  applied  to  the  drawing,  the  most  common  of 
which  is  a  process  called  Across-hatching." 

28.  Cross-hatching. — In    drawing,  to   cross-hatch    means    to 
rule  the  drawing  with  straight  lines,  usually  at  forty-five  degrees 
to  the  horizontal,  thus  indicating  that  the   drawing  is  a  repre- 
sentation of  a  cut  portion  and,  at  the  same  time,  indicating  the 
kind  of  material  by   the   arrangement  of  the  lining — different 
materials  being  represented  by  different  cross-hatchings.     (See 
Standard  Cross-hatchings,  page  179.) 

When  two  pieces  of  the  same  material  are  shown  together 
in  a  drawing,  the  cross-hatching  should  have  different  directions, 
being  usually  "hatched"  at  right  angles.  When  three  or  more 


12  MECHANICAL   DRAWING. 

pieces  of  the  same  material  are  shown  together,  no  two  pieces 
should  have  the  same  angle  and  direction.  When  two  pieces  of 
different  materials  are  shown  together,  the  distinction  is  indicated 
by  the  different  lining,  though  it  is  desirable  to  make  the  drawing 
more  readable  by  changing  the  direction  of  the  cross-hatching 
also.  When  three  or  more  pieces  of  different  materials  are  shown 
together,  it  is  best  to  have  a  new  direction  for  the  cross-hatching 
of  each. 

29.  Lines. — Since  drawings  consist  of  different  kinds  of  lines 
it  is  well  to  give  a  specific  name  to  each  kind. 


LINES  AND  THEIR  WEIGHTS. 


Light. 

Medium. 

Heavy. 

Center  lines. 


LINES  OF  THE  DRAWING. 
Full.  Dashed  Dotted. 


Lighter  than  lines  of  the  drawing. 

Section  lines. 

Heavier  than  lines  of  the  drawing. 

Dimension  lines. 


Lighter  than  lines  of  the  drawing. 

Border  lines,  top  and  left  hand  lines  to  be  of  medium  weight, 
bottom  and  right  hand  lines  to  be  heavy  lines. 


30.  Lines  of  the    Drawing. — Those  lines  which  go  to  make 
up  the  drawing  of  an  object  are  called  lines  of  the  drawing  and 
may  be  either  full  or  broken  lines,  light  or  heavy,  entire  or  in 
combinations. 

31.  Border  Lines. — Border  lines  are  lines  which  are  drawn 
about  a  drawing  inclosing  it  after  the  manner  of  a  picture-frame, 
and  are  usually  straight  lines  forming  a  rectangle.    They  vary 
greatly,  however,  as  border  lines  are  often  of  original  design. 

32.  Center     Lines. — Center    lines    are    broken    lines    drawn 
through  the  center  of  a  drawing  or  drawings,  as  the  case  may 


ELEMENTARY  PRINCIPLES  AND  DEFINITIONS.  i3 

be,  and  are  used  to  "align"  the  different  views — to  produce 
an  axis  of  symmetry.  When  two  center  lines  are  employed,  they 
are  usually  at  right  angles,  one  being  horizontal  and  one  vertical. 
Center  lines  are  used  only  on  such  drawings  as  naturally  seem 
to  require  them,  that  is,  on  drawings  of  turned  work  and  on  those 
which  can  be  symmetrically  divided  by  such  lines.  (See  Figs. 
5  and  6.) 


FIG.  5 
Such  Drawings  require  the  Use  of  Center  Lines. 


FIG.  6 
Such  Drawings  require  no  Center  Lines. 

33.  Section  Lines. — Section  lines  are  broken  lines  carried 
through  the  drawing  to  indicate  the  line  (plane)  on  which  the 
section  has  been  taken — the  line  on  which  the  object  has  been 

cut. 


14  MECHANICAL  DRAWING. 

34.  Construction  Lines. — Construction  lines  are  auxiliary  lines 
used  in  the  construction  of  the  drawing  and  usually  do  not  appear 
on  the  finished  drawing. 

35.  Projection  Lines. — Projection  lines  are  construction  lines, 
usually  horizontal  or  vertical,  or  both,  and  are  used  to  project 
from  one  view  to  another.     The  horizontal  limiting  lines  for  all 
elevations  and  the  vertical  limiting  lines  for  plan,  elevation,  and 
bottom  are  examples  of  projection  lines. 

36.  Dimension  Lines. — Dimension  lines  are  broken  lines  ter- 
minating   in   arrow-heads   which,    together   with   figures,   when 
added  to  the  drawing  enable  the  observer  to  read  the  sizes  of 
the  various  parts. 

37.  Guide  Lines. — Guide  lines  are  light  pencil  lines  used  as 
guides  in  lettering. 

38.  Light  and  Shade. — Without  light  and  shade  a  drawing  is 
merely  a  flat  outline.     It  is  often  necessary  and  at  times  quite 
desirable  to  give  the  drawing  some  projection,  to  cause  it  to  "stand 
out"  from  the  paper,  to  give  it  relief,  in  which  case  it  is  neces- 
sary to  introduce  light   and  shade;    this  is  called  "shading  the 
drawing." 

The  shading  of  drawings  is  rarely  resorted  to  for  drawings 
representing  flat  surfaces,  being  most  helpful  when  applied  to 
drawings  representing  curved  surfaces. 

39.  Line  Shading. — Line  shading  is  lining  the  drawing  with 
lines  of  varying  weights,  and  spacings. 

In  all  drawing  the  rays  of  light  are  assumed  to  strike  the  plane 
of  the  paper  at  an  angle  of  forty- five  degrees,  usually  taken  as 
coming  from  the  left.  If  a  surface  is  uniformly  covered  with 
light,  it  is  said  to  be  in  the  light;  if  uniformly  covered  by  a  shadow, 
it  is  said  to  be  in  the  shadow.  From  the  former  to  the  latter 
there  are  all  degrees  of  light  and  shade — from  that  point  at  which 
the  rays  of  light  are  reflected  by  the  object  to  the  observer's  eye, 
which  is  called  the  brilliant  point,  to  that  point  from  which  all 
rays  of  light  are  obscured. 

40.  Shade  or  Shadow  Lining. — Shadow  lines   are  lines  repre- 
senting those  surfaces  of  an  object  which  are  in  the  shadow.    The 


ELEMENTARY  PRINCIPLES  AND  DEFINITIONS.  15 

application  of  shade  or  shadow  lines  to  drawings  is  the  practical 
method  of  "shading"  drawings,  the  convention  being  as  follows: 
Assume  the  drawing  to  be  the  object  itself,  and  assume  the  parallel 
rays  of  light  to  extend  across  the  plane  of  the  paper  and  as  coming 
from  the  upper  left-hand  direction,  that  is,  from  the  top  and  left 
sides  of  the  paper;  then  make  those  lines  heavy  which  represent 


FIG.  7  FIG.  8 

Lines  of  Uniform  Weight.  Shade  Lined. 

A  MECHANICAL  DRAWING  OF  A  FLAT  PLATE. 


FIG.  10 
Lines  of  Uniform  Weight.  Shade  Lined. 

A  MECHANICAL  DRAWING  OF  A  RING. 

surfaces  from  which  the  light  is  excluded — a  process  which  is 
sometimes  called  "  back- lining. "     (See  Figs.  7,  8,  9,  and  10.) 

It  is  obvious  that  the  right-hand  and  bottom  lines,  for  draw- 
ings representing  solid  objects,  and  the  upper,  or  top,  and  left-hand 
lines,  on  drawings  of  interior  features — holes,  etc. — are  the  proper 
lines  to  shade. 


i6 


MECHANICAL   DRAWING. 


41.  Drawing  to  Scale. — In  mechanical  drawing  the  drawings 
are  usually  drawn  to  scale,  that  is,  the  drawing  is  made  to  be 
of  the  same  size  as  the  object  or  some  proportional  size  thereof. 
When  possible  it  is  best  to  make  the  drawing  full  size — the  same 
dimensions  as  the  object;   in  any  case,   however,   it  is  well  to 
choose  such  a  scale  as  will  make  the  drawing  as  large  as  possible. 
The  usual  scales  are  full  size,  three-fourths  size,  one-half  size,  and 
one-quarter  size  for  comparatively  small  objects,  and'  for  those 
of    large   dimensions  one-eighth   size,    one- twelfth   size,   one-six- 
teenth   size,   one-twenty-fourth    size,   one- thirty- sixth    size,    one- 
forty-eighth  size,  etc. 

42.  Choosing  the  Scale. — In  choosing  the  scale  for  any  partic- 
ular drawing  there  are   three   things  to  be  considered:    (i)  the 


THE  OBJECT  TO  BE  DRAWN 
Fig.  11 

dimensions  of  the  object  to  be  drawn,  (2)  the  dimensions  of  the 
sheet  of  paper  on  which  the  drawing  is  to  be  made,  and  (3)  the 
number  of  views  to  be  drawn.  With  these  known  we  have  the 
full  size  of  the  drawing  known,  not  only  of  any  one  view  alone, 
but  of  the  several  views  collectively — the  mechanical  drawing  of  the 


ELEMENTARY  PRINCIPLES  AND  DEFINITIONS.  17 

object — and  the  size  of  the  sheet  of  paper  to  receive  the  drawing; 
it  is  then  a  simple  matter  to  calculate  the  largest  scale  possible 
to  fit  the  conditions. 

EXAMPLE. — Let  Fig.  n  represent  the  object  to  be  drawn,  let 
Fig.  12  represent  the  sheet  of  paper  to  receive  the  drawing — it 


Fig.  12 

being  the  standard  sheet  for  the  exercises  of  the  Course — and 
let  it  be  required  to  draw  three  views:  (i)  a  plan,  (2)  a  side  eleva- 
tion, and  (3)  an  end  elevation. 

Assuming  the  object  to  be  inclosed  within  a  rectangular  box 
as  indicated  by  the  figure  A-B-C-D-E-F-G-H,  note  that  the  plan, 
or  top  view,  is  inclosed  within  a  rectangle  which  is  2o"Xn"  in 
dimensions,  that  the  side  elevation  is  inclosed  within  a  rectangle 
the  dimensions  of  which  are  2o"Xi2",  and  that  the  end  elevation 
is  inclosed  within  an  n"Xi2"  rectangle.  (See  Fig.  13.) 

As  to  arrangement,  it  is  fundamental,  of  course,  that  the 
long  dimension  of  the  drawing  should  be  placed  according  to 
the  long  dimension  of  the  sheet  to  receive  the  drawing;  this 
dimension  (of  the  drawing)  is  the  sum  of  the  length  of  the  side 
elevation  and  the  width  of  the  end  elevation  and  is  31".  The 
short  dimension  of  the  drawing  is  the  sum  of  the  height  of  the 
side  elevation  and  the  width  of  the  plan  and  is  23".  A  full-size 
drawing,  then,  would  occupy  a  space  3i"X23";  the  space  to 
receive  the  drawing  is  8"Xn".  With  these  figures  known  it  is 


i8 


MECHANICAL  DRAWING. 


simply  a  problem  in  arithmetic  to  reduce  the  dimensions  of  the 
full-size    drawing  to  fit  the  paper;    the  largest  size  possible  is 

B  C  C  G 


PLAN 


B 


END  EL. 


H 


Fig.  13 


SIDE  EL. 


evidently  one-quarter  size,  7l"X5f",  and  to  fit  the  conditions 
let  the  drawings  be  arranged  as  in  A,  Fig.  14. 


FIG..  14 

43.  Balance  and  Symmetry  of  a  Drawing. — A  correct  me- 
chanical drawing  of  an  object  can  be  made  and  yet  not  present 
a  very  good  appearance.  The  appearance  of  a  drawing  is  a 
large  measure  of  its  value,  and  the  draughtsman  who  would  be 
successful  should  exercise  due  care  to  execute  well-appearing, 
correct  drawings. 

The  essentials  for  a  well-appearing  drawing  are:  a  neat, 
clean-cut  drawing  of  the  various  views,  neat  and  well-made 


ELEMENTARY  PRINCIPLES  AND  DEFINITIONS.  19 

lettering,  the  dimensions  carefully  planned,  and  the  whole  so 
placed  on  the  paper  as  to  present  a  well-balanced  effect  with 
respect  to  the  border  lines  and  with  one  another,  and  a  symmetry 
with  any  and  all  center  lines  that  may  be  used  on  the  drawing. 

A  careful  draughtsman  will  calculate  the  "  balance"  of  his  sheet 
— the  space  between  views  and  between  the  drawing  and  the 
border  lines — before  beginning  the  drawing,  a  good  general  rule 
for  which  is  as  follows:  First  decide  upon  the  number  of  views 
to  be  drawn;  second,  decide  upon  the  arrangement  of  the  views; 
third,  calculate  the  space  required  for  the  drawing;  fourth, 
ascertain  the  dimensions  of  the  sheet  of  paper  to  receive  the 
drawing;  fifth,  subtract  the  dimensions  of  the  space  required 
for  the  drawing  from  those  of  the  space  available;  and  sixth, 
divide  the  remainders  by  the  number  of  the  respective  spaces 
to  be  provided. 

EXAMPLE. — Let  it  be  required  to  calculate  the  "balance"  for 
the  conditions  given  in  the  example  of  section  42.  To  begin 
with,  the  space  required  for  the  drawing  (7|"X5|"),  the  space 
available  (8"  X  n"),  and  the  arrangement  of  the  views  (4,  Fig.  14) 
are  known. 

An  inspection  of  the  arrangement  shows  that  there  are  three 
spacings  each  way  (horizontally  and  vertically)  to  be  provided: 
(i)  a  space  between  views  and  (2  and  3)  a  space  between  the 
drawing  and  the  border  line  of  the  sheet.  To  get  the  horizontal 
spacing,  subtract  the  horizontal  dimension  (7  j")  of  the  drawing 
from  the  horizontal  dimension  (n")  of  the  sheet  and  divide  the 
remainder  (3^")  by  three;  when  the  remainder  does  not  divide 
evenly,  as  in  this  case,  a  compromise  may  be  arranged  as  is  shown 
in  Fig.  14.  To  obtain  the  vertical  spacing,  subtract  the  vertical 
dimension  (5!")  of  the  drawing  from  the  vertical  dimension  of 
the  sheet  and  divide  the  remainder  (2^")  by  three. 

44.  Flexibility  of  the  Drawing. — It  seems,  at  first  thought,  a 
strange  and  very  unnecessary  procedure  that  certain  rules  be 
given  for  the  proper  arrangement  of  the  views  of  a  drawing,  as 
has  been  done  in  the  first  part  of  these  notes,  and  then  to  depart 
from  their  literal  meaning,  as  is  done  in  Fig.  14. 


20  MECHANICAL   DRAWING. 

The  arrangement  given  in  Fig.  i,  Plate  No.  i,  is  the  proper 
and  most  clearly  understood  arrangement,  and  should  be  adhered 
to  when  possible.  In  the  construction  of  a  drawing,  the  limits 
of  the  paper  and  reserved  spaces — space  for  title,  notes,  etc. — 
are  important  factors  to  be  considered,  and  for  the  most  economi- 
cal use  of  the  sheet  the  drawing  should  be  so  made  that  it,  to- 
gether with  the  lettering,  the  title  and  notes,  will  completely  fill 
the  sheet  and  the  whole  be  made  to  present  a  full  and  well-bal- 
anced appearance.  To  do  this  it  is  often  necessary  to  violate 
the  given  rules  and  to  make  the  arrangement  to  fit  the  condi- 
tions— it  must  be  flexible. 

A  clear  understanding  of  the  rule  is  first  necessary,  and  having 
the  underlying  principles  well  in  hand  it  will  always  be  a  simple 
matter  to  adjust  the  drawing  to  fit  any  and  all  conditions  and 
yet  fulfill  the  requirements  for  a  correct  mechanical  drawing. 
For  this  reason  the  rule  is  given  and  should  receive  due  con- 
sideration. 

The  first  requirement  of  a  mechanical  drawing  is  to  "show" 
the  object,  and  any  arrangement  which  does  this  clearly  is  a 
correct  arrangement. 

45.  Dimensioning. — Dimensioning  is  one  of  the  most  impor- 
tant and  widely  discussed  details  of  mechanical  drawing,  each  and 
•every  shop  using  that  'system  which  works  out  most  satisfac- 
torily for  its  particular  work.  Some  shops  use  the  decimal  sys- 
tem— " engineer's  scale"  (sect.  100) — giving  the  dimensions  in 
hundredths  parts  of  the  unit  used,  as  .09  of  an  inch,  the  inch  being 
the  unit.*  Other  shops  use  the  "architect's  scale,"  giving  the 
dimensions  as  J  inch,  \  inch,  J  inch,  etc.,  the  inch  being  the  unit 
used,  and  this  is  the  system  most  widely  in  use.  Again,  some 
shops — mostly  in  boiler- work — give  dimensions  in  inches  entirely, 
as  1 08  inches,  while  other  shops  use  feet  and  inches,  as  10  feet 
4  inches,  which  latter  system  is  the  one  usually  used,  and  this, 
in  turn,  is  varied  when  the  dimension  to  be  given  is  an  even 
number  of  feet,  some  draughting- rooms — notably  those  of  bridge 

*  This  explanation  is  with  reference  to  American  practice,  the  inch  being  the 
unit  adopted  in  the  United  States. 


ELEMENTARY  PRINCIPLES  AND  DEFINITIONS.  21 

and  plate  works — giving  it  as  19  feet  o  (zero)  inches,  and  others 
— manufacturers  of  machinery — simply  19  feet,  no  mention 
being  made  of  the  inches.  It  is  universally  agreed,  however, 
that  all  dimensions  under  three  feet  should  be  given  in  inches, 
and  those  greater  than  three  feet  to  be  given  at  the  draughts- 
man's discretion. 

In  most  shops  certain  notation  is  used  to  indicate  feet  and 
inches,  some  shops  using  the  abbreviations  "ft."  for  feet  and 
"in."  for  inches;  others  use  one  dash,  thus  ',  for  feet,  and  two 
dashes,  thus  n ',  for  inches,  while  some  shops  give  all  dimensions 
in  inches  and  with  that  understanding  omit  all  such  notation. 
Another  method  is  to  write  "ft."  for  feet  and  use  the  two  dashes 
(")  for  the  inches.  The  dashes  for  both  feet  and  inches  is  the 
usual  practice. 

In  putting  on  dimensions  those  figures  representing  the  full 
size  of  the  object  are  given  and  a  note  added  as  to  the  scale  of 
the  drawing,  and  not  figures  representing  the  size  of  the  drawing 
unless  it  be  a  full-size  drawing,  when,  of  course,  the  dimensions 
of  the  drawing  and  of  the  object  are  the  same;  in  any  case  a  note 
as  to  the  scale  used  should  be  on  the  drawing. 

46.  Selection  of  the  Necessary  Views. — Thus  far  six  views 
of  an  object  have  been  dealt  with:  plan,  front,  right,  left,  and 
rear  elevations,  and  bottom  view.  Very  rarely  is  this  number 
necessary  to  show  an  object:  a  lesser  number  being  usually  suffi- 
cient. The  selection  of  the  proper  views  and  their  number  is  of 
primary  importance,  and  it  is  here  that  the  draughtsman  must 
exercise  his  ingenuity  and  knowledge  of  shop  practice.  First  of 
all  the  drawing  must  tell  the  story,  it  must  clearly  show  the  object, 
and  the  least  number  of  views  which  does  this  is  the  correct 
number  to  use. 

In  the  selection  of  what  views  should  be  drawn  the  draughts- 
man should  consider  the  purpose  of  the  drawing.  If  it  is  for  shop 
purposes — a  shop  drawing — it  should  be  complete  in  every  detail; 
for  example,  if  it  be  a  drawing  of  a  single  piece  of  a  machine — a 
detail — the  draughtsman  should  place  himself  in  the  shopman's 
position  and  should  consider  just  what  is  necessary  to  show 


22  MECHANICAL  DRAWING. 

the  piece,  what  would  he  have  to  know  to  produce  it,  what 
views  are  necessary  to  portray  every  feature,  what  dimensions, 
what  notes,  etc.  If  it  be  an  assembled  drawing  for  erectional  pur- 
poses, let  the  draughtsman  assume  the  position  of  the  erecting 
workman,  and  consider  what  drawings,  dimensions,  notes,  etc., 
would  be  necessary  to  carry  out  the  work. 

47.  Usual  Number  of  Views. — For  simple  objects,   a  plan, 
one  elevation  and  a  sectional  view,  or  two  elevations  and  a  section, 
properly  noted  and  dimensioned,  is  all  that  is  necessary  to  clearly 
define  the  object.     For  complex  objects  the  views  range  in  num- 
ber from  either  of  the  above  combinations  to  a  drawing  composed 
of  a  plan  and  bottom  view,  four  elevations,  and  any  number  of 
sections. 

48.  Use  of  Dashed  and  Dotted  Lines  to  Reduce  the  Number 
of  Views. — In  manufacturing  the  draughting- room  is  a  means  to 
an  end.      From  the  draughtsman's  standpoint  the  number  of 
views  constituting  a  drawing  should  be  as  small  as  possible; 
from   the   workman's — the  shopman's — standpoint  the  drawing 
should  be  as  elaborate  and  complete  as  possible.     A  mean  of  these 
two  extreme?  is  the  usual  practice,  and  to  assist  the  draughtsman  he 
is  allowed  to  use  dashed  and  dotted  lines  to  indicate  hidden  features. 

The  compromise  is  quite  satisfactory  for  comparatively  simple 
objects  and  oftentimes  may  decrease  the  labor  of  making  a  legible 
drawing  by  one-half;  it  is,  however,  very^  desirable  that  dashed 
and  dotted  lines  be  reserved  for  simple  drawings,  as  for  the  more 
elaborate  ones  they  prove  very  confusing;  in  such  drawings  they 
should  be  omitted  and  other  views  and  sections  added. 

49.  Beginning  to  Draw. — When  a  cTrawing  is  to  be  made,  the 
first  thing  to  be  considered  is  the  purpose  of  the  drawing;   with 
this  well  in  mind  carefully  study  the  object  to  be  drawn  and 
decide  upon  the  least  number  of  views  it  will  be  necessary  to 
draw  to   clearly  define  the  object.     Having   decided  upon  the 
number  of  views  to  be  drawn,  consider  the  size  of  the  sheet  of 
paper  to  receive  the  drawing  and,  in  accordance  with  section  42, 
select  the  largest  scale  possible  under  the  conditions.     With  the 
dimensions  of   the  drawings  known,  the  margin  between  them 


ELEMENTARY  PRINCIPLES  AND  DEFINITIONS.  23 

and  the  border  lines  and  the  spaces  between  one  another  may  be 
calculated  and  the  drawing  balanced  without  a  line  being  drawn; 
this  done  the  drawing  may  be  begun.  Do  all  thinking  and 
planning  with  few  preliminary  lines,  know  what  to  do,  how  it 
is  to  be  done,  and  then  proceed  with  the  work. 

50.  Draughting-room  Practice.  —  In  ordinary  commercial 
draughting  one  meets  with  two  kinds  of  mechanical  drawing: 
(i)  sketches  which  are  used  for  preliminary  purposes — temporary 
drawings— and  (2)  the  valuable  permanent  drawings  which  are 
placed  on  file  and  carefully  preserved. 

Sketches  are  usualy  made  in  pencil — though  pen  and  ink 
are  sometimes  used — and  are  usually  free-hand  drawings.  The 
permanent  drawings  are  constructed  with  a  view  to  reproduction, 
the  usual  procedure  being  as  follows: 

A  pencil  drawing  is  first  carefully  constructed  on  some  medium 
grade  of  paper,  and  from  this  pencil  drawing  a  tracing  is  made 
in  water- proof  ink  on  tracing-cloth,  or  tracing-paper  (the  former 
is  preferable),  and  from  this  tracing  a  blue-print  is  made. 

Draughting-rooms  are  like  individuals,  each  has  its  own 
particular  method  for  the  accomplishment  of  its  purpose,  the 
purpose  of  a  draughting-room  being,  primarily,  to  construct  draw- 
ings; all,  however,  agree  on  a  general  method  of  procedure  which 
may  be  condensed  to  the  following: 

Drawings  must  be  clear  and  concise. 

Drawings  must  be  complete. 

Drawings  should  have  all  dimensions  given — total  dimen- 
sions and  of  all  parts — no  addition,  division,  or  subtraction  being 
left  to  the  shopman. 

Drawings  should  be  confined  to  small  sheets. 

Drawings  should  be  grouped,  that  is,  things  of  a  kind  should 
be  placed  on  a  sheet  of  the  kind;  as,  drawings  of  pieces  to  be 
forged  should  be  placed  on  a  "sheet  of  forgings";  all  brasswork 
should  be  together,  all  cast-iron  parts  should  be  drawn  by  them- 
selves, etc. 

Draughtsmen  should  show  a  knowledge  of  the  work  they 
propose;  how  each  piece  is  to  be  produced;  as,  holes  to  be  cored 


24  MECHANICAL  DRAWING. 

should  be  so  marked;  holes  to  be  drilled  should  be  marked  "to 
be  drilled";  holes  to  be  drilled  and  tapped  should  have  the  size 
of  drill  and  tap  given;  surfaces  to  be  finished  should  be  marked 
"to  be  finished";  the  number  wanted  of  each  piece  and  kind  of 
material  should  be  noted,  etc. 

51.  The  Time  Element  in  Drawing. — Rapid  execution  of 
drawings  is  demanded  by  all  firms,  and  the  ability  to  execute  a 
clean-cut,  well- appearing  drawing  within  a  short  time  is  the 
measure  of  a  draughtsman's  worth.  The  beginner  should  remem- 
ber the  value  of  time  in  the  execution  of  his  work  and  should 
strive  to  produce  a  legible  drawing  in  the  shortest  time  possible; 
this,  however,  not  to  be  at  the  expense  of  the  quality  of  the  work. 
Quality  without  quantity  means  limited  pay  and  a  secondary 
position;  quantity  without  quality  is  a  similar  condition;  while 
quantity  and  quality  is  the  correct  combination  and  means  the 
highest  salary  and  most  responsible  position. 

In  acquiring  the  art  of  draughting  careful  search  should  be 
made  to  find  ways,  means,  and  "kinks"  with  which  to  expedite 
the  work  if  possible.  Of  these  "labor-saving  devices,"  besides 
special  tools  and  other  mechanical  means,  mention  may  be  made 
of  free-hand  lettering  and  of  certain  conventions,  some  of  which 
are  universally  adopted  and  others  which  pertain  to  a  particular 
line  of  work. 

Free-hand  lettering  being  so  far  in  advance  of  mechanical 
lettering  as  regards  time  required  in  its  execution  needs  no  other 
argument  as  to  the  "why"  of  its  desirability. 

The  laborious,  time-consuming,  and  erstwhile  universal  method 
of  cross-hatching  sections  with  lines  in  certain  arrangements  to 
indicate  cut  portions  and  kinds  of  materials  is,  of  late  years,  being 
discarded  in  a  large 'number  of  shops  for  other  conventions 
more  convenient  and  rapid  of  application.  Some  shops  use  no 
cross-hatching  whatever,  simply  marking  the  drawings  C.  I.  for 
cast  iron,  W.  I.  for  wrought  iron,  S.  for  steel,  etc.,  and  indicating 
cut  portions  by  darkening  that  portion  of  the  drawing  with  a 
lead-pencil  or  other  quickly  applied  medium,  as  by  coloring  the 
sections  with  brush  and  water  colors. 


ELEMENTARY  PRINCIPLES  AND  DEFINITIONS.  .25 

There  are  a  great  number  of  minor  labor-saving  kinks,  many 
presenting  themselves  to  ingenious  draughtsmen,  but  to  the 
student  suffice  it  to  again  advise  a  sharp  outlook  for  these  things. 

52.  Conventions. — To  construct  every  detail  of  a  drawing 
theoretically  exact  would  consume  much  valuable  time,  and  to 
expedite  the  work  certain  conventions  are  adopted.  Every  class 
of  drawing — bridge  drawing,  the  drawings  used  in  electrical  work, 
etc. — has  its  particular  and  peculiar  conventions;  also,  different 
firms  engaged  in  the  same  line  of  work  often  use  conventions 
peculiar  to  themselves.  There  are,  however,  a  large  number  of 
simple  conventions — fundamentals — such  as  screw-threads,  breaks, 
methods  for  indicating  sections,  the  kind  of  material,  etc.,  that 
are  common,  with  possibly  slight  variations  in  certain  cases.  A 
number  of  these  are  given  in  the  accompanying  drawings  and 
should  be  noted. 


CHAPTER  II. 

LETTERS,  FIGURES,  AND  LETTERING. 

53.  Fundamentals. — Lettering  is  to  a  drawing  what  clothes 
are  to  a  man — it  makes  the  appearance,  and  appearance  is  of 
much  importance  to  a  drawing.  A  drawing  may  be  correct  in 
all  its  details  and  yet  present  a  poor  appearance,  but  a  well- 
appearing,  correct  drawing  is  what  manufacturers  want  and  are 
willing  to  pay  for;  therefore  the  ability  of  a  draughtsman  to  do 
good  lettering  is  a  measure  of  his  worth.  The  study  of  lettering, 
then,  becomes  of  prime  importance  to  the  student  of  mechanical 
drawing. 

A  drawing  may  be  "  made  or  marred "  in  the  lettering,  hence 
great  care  should  be  exercised  in  the  lettering  of  it,  and  that  letter 
which  can  be  most  rapidly  made,  which  looks  well  when  made 
and  in  any  size,  should  be  selected  for  the  work.  A  letter  to  fulfill 
these  conditions  must,  obviously,  be  one  of  simple  outline,  thus 
minimizing  and  expediting  the  labor  of  its  execution,  and  being 
free  from  ornamentation  it  presents  a.  clear  outline  and  is  readily 
legible. 

The  letter  most  widely  accepted  as  meeting  these  conditions 
is  what  is  known  as  the  "Gothic  Alphabet."  Of  this  letter  there 
is  the  upper  case,  or  capital  letters,  and  the  lower  case,  or  small 
letters;  these  may  be  vertical  or  inclined,  which  gives  practically 
four  alphabets  and*  is  quite  sufficient  for  all  usual  commercial 
draughting. 

The  Gothic  alphabet  may  be  constructed  free-hand  or  with 
instruments,  and  may  be  a  single-line  letter  or  a  heavy  letter 
made  up  of  heavy  lines,  several  "single"  lines  in  thickness.  To 
construct  the  letters  with  instruments — mechanically — consumes 

26 


LETTERS,  FIGURES,  AND  LETTERING.  27 

too  much  time  for  practical  work  and  the  beginner  should  devote 
his  attention  to  the  free-hand  alphabet. 

To  acquire  the  ability  to  execute  neat  and  well-appearing 
free-hand  letters,  the  student  should  first  carefully  study  the 
standard  proportions  and  characteristics  of  the  various  letters 
and  then  practice  their  construction.  Much  care  and  pains  must 
be  taken  with  these  preliminaries,  as  lettering  is  an  art  which 
cannot  be  mastered  in  a  few  hours,  but  requires  perseverance 
and  practice.  When  the  individual  letters  have  been  mastered 
to  a  degree,  the  construction  of  words  may  be  taken  up. 

The  spacing  of  the  various  letters  which  go  to  make  up  a 
word  now  enters  into  the  subject  and  is  a  very  important  factor. 
The  letters  should  be  placed  as  near  one  another  as  is  consistent 
with  clearness  (about  one- sixteenth  to  one-sixty-fourth  of  an 
inch  apart),  thus  giving  the  arrangement  a  well- grouped  and 
compact  appearance.  Each  letter  should  be  of  the  same  alpha- 
bet— upper  or  lower  case,  vertical  or  inclined — of  the  same  size 
(initial  letters  excepted)  and  uniformly  spaced.  Much  considera- 
tion of  the  dimensions  of  the  various  letters,  together  with  spacing 
and  a  large  amount  of  practice,  is  necessary  at  this  point. 

Having  acquired  the  ability  to  execute  words  in  a  rapid, 
neat,  and  well-appearing  manner,  the  student  is  ready  to  execute 
sentences,  and  now  the  spacing  of  words  demands  attention. 
Words  should  be  placed  according  to  the  space  they  are  to  occupy; 
ordinarily,  however,  they  should  be  from  one- eighth  to  one- 
quarter  of  an  inch  apart,  the  letters  of  each  word  being  so  grouped 
that  the  words  are  quite  compact,  and  this  small  space  between 
words  sufficient  to  cause  them  to  stand  out  and  be  easily -read. 

In  all  lettering  much  care  should  be  exercised  to  produce  a 
regular  and  uniform  effect,  that  is,  the  individual  letters  of  words 
should  be  neither  cramped  nor  isolated,  enlarged  or  decreased  in 
size,  but  the  whole  so  constructed  as  to  secure  a  well-balanced 
and  uniform  word.  This  matter  of  regularity  and  uniformity 
is  the  "  secret "  of  good  lettering  and  applies  not  only  to  words 
but  to  entire  sentences  and  groups  of  sentences  as  well. 

After  the  student  has  acquired  a  working  knowledge  of  the 


28 


MECHANICAL   DRAWING. 


foregoing  fundamental  requirements,  from  thence  on  his  letter- 
ing becomes  a  matter  of  practice,  and  as  "practice  makes  perfect " 
too  much  time  cannot  be  devoted  to  it. 

54.  A  Study  of  Letters. — Taking  up  the  upper- case  Gothic 
Alphabet,  attention  should  be  given  to  the  proportions  and  char- 
acteristics of  each  letter,  together  with  the  manner  of  its  con- 
struction. The  most  popular  style  of  this  alphabet  is  the  "  square  " 
letter,  so  called  because  the  major  portion  of  the  alphabet  may 
be  constructed  within  a  square. 

The  vertical  type  of  the  upper-case,  square  Gothic  alphabet 
is  used  for  illustration,  though  the  remarks  given  apply,  also, 
to  the  inclined  type  of  the  same  alphabet. 

The  letter  A,  constructed  in  the  manner  indicated — 
the  arrows  indicating  the  direction  of  the  stroke  and 
the  figures  the  order  in  which  the  strokes  are  made — 
has  equal  width  and  height  for  proportions,  and  is 
characterized  by  the  horizontal  bar,  stroke  3,  which  is 
below  ths  horizontal  center  line  through  the  square. 
In  the  inclined  letter,  alphabet  No.  3,  Plate  No.  3, 
note  that  stroke  2  is  vertical. 

Proportions,   the  height  equals  the  width;    char- 
acteristics, bars  2,  3,  and  6  are  horizontal,  the  upper 
I  g—3^  43J    part  0£  the  }etter  is  smaller  than  the  lower  part — 
J*~-  v~Sf  stroke  3  is  above  the  center  of  the  square — and  arcs  4 
and  5  are  arcs  of  circles.     In  the  inclined  letter  strokes 
4  and  5  are  elliptical  arcs. 

Proportions,  the  height  equals  the  width;  char- 
acteristics, all  of  the  arcs  are  circular  arcs,  and  the 
lower  terminus  of  the  letter  extends  farther  to  the 
right  than  the  upper  terminus,  thus  giving  the  letter  a 
kind  of  base.  In  the  inclined  letter  the  arcs  are 
elliptical. 

Proportions,  the  height  equals  the  width;  char- 
acteristics, bars  2  and  3  are  horizontal,  and  stroke  4 
is  the  arc  of  a  circle.  In  the  inclined  letter  this  stroke 
is  the  arc  of  an  ellipse. 


LETTERS,  FIGURES,  AND   LETTERING.  29 

Proportions,  the  height  equals  the  width;  char- 
acteristics, three  horizontal  bars,  the  bottom  bar 
slightly  longer  than  the  upper  bar — to  give  the  letter 
a  base — and  bar  4  is  above  the  center  of  the  square 
and  from  one -half  to  two- thirds  the  length  of  the  top 
bar. 

Proportions,  the  height  equals  the  width;  char- 
acteristics, bars  i  and  2  are  equal  in  length,  and  bar  3 
is  above  the  center  of  the  square  and  from  one-half 
to  two- thirds  the  length  of  bar  2. 

Proportions,  the  height  equals  the  width;  char- 
acteristics, the  arcs  are  arcs  of  circles,  bar  2  is  on 
the  horizontal  center  line  and  extends  a  trifle  to  the 
right  of  the  terminus  of  arc  3.  In  the  inclined  letter  the 
arcs  are  elliptical. 

Proportions,  the  height  equals  the  width;  char- 
acteristics, the  side  lines  are  parallel,  and  the  cross-bar 
is  above  the  center  of  the  square. 

Proportions,  the  height  equals  the  height  of  the 
square;  the  width  equals  the  width  of  the  line.  (Note 
that  I  is  the  first  letter  in  which  the  height  and  the 
width  are  unequal.)  Characteristic,  it  is  a  simple 
straight  line.  The  upper- case  I  is  not  dotted. 

Proportions,  the  height  equals  the  width;  char- 
acteristics, the  arcs  are  the  arcs  of  a  circle,  and  the 
left  terminus  does  not  extend  quite  up  to  the  center 
line.  The  letter  J  is  often  misconstructed,  being 
sometimes  turned  backwards;  also,  one  is  apt  to  make 
it  too  narrow  and  thus  spoil  its  proportions;  care 
should  be  exercised  not  to  extend  the  left-hand  ter- 
minus, stroke  2,  above  the  center  line,  else  the  letter 
will  be  confused  with  the  letter  U.  In  the  inclined 
letter  the  arcs  are  elliptical. 


3° 


MECHANICAL  DRAWING. 


Proportions,  the  height  equals  the  width;  char- 
acteristics, bar  2  extends  from  a  point  not  quite  to 
the  corner  of  the  square  to  a  point  below  the  inter- 
section of  the  center  line  of  the  square  and  the  vertical 
bar.  Bar  3  joins  bar  2  above  the  center  and  extends 
to  the  lower  corner  of  the  square. 

Proportions,  the  height  equals  the  width;  char- 
acteristics, bars  i  and  2  are  of  equal  lengths  and  occupy 
two  sides  of  the  square.  This  letter  is  sometimes 
made  backwards.  Note  the  proper  way  of  drawing 
bar  2. 

Proportions,  the  width  is  from  one-fourth  to 
one-third  greater  than  the  height  of  the  letter, 
making  M  the  widest  letter  thus  far;  character- 
istics, the  side  lines  are  parallel  and  the  diagonals, 
3  and  4,  are  of  equal  lengths.  This  letter  is  often 
made  as  the  letter  W  would  appear  if  inverted, 
and  when  so  constructed  is  incorrect. 

Proportions,  the  height  equals  the  width;  char- 
acteristics, the  side  lines  are  parallel  and  the  diagonal 
extends  from  the  upper  left-hand  corner  of  the  square 
to  the  lower  right-hand  corner. 

Proportions,  the  height  equals  the  width;  char- 
acteristic, it  is  a  complete  circle.  In  the  inclined 
letter  it  becomes  an  ellipse. 

Proportions,  the  height  equals  the  width;  char- 
acteristics, strokes  2  and  3  are  horizontal,  the  lower 
one,  3,  is  below  the  center  of  the  square,  and  the  arc 
is  the  arc  of  a  circle.  In  the  inclined  letter  the  arc  is 
elliptical. 

Proportions,  the  height  equals  the  width;  char- 
acteristic, it  is  a  complete  circle,  same  as  the  letter  O 
with  the  addition  of  stroke  3.  In  the  inclined  letter 
the  circle  becomes  an  ellipse. 


LETTERS,  FIGURES,  AND  LETTERING.  31 

Proportions,  the  height  equals  the  width;  char- 
acteristic, it  is  the  same  as  the  letter  P  with  the  addi- 
tion of  stroke  5.  The  letters  P  and  R  are  two  of  the 
"hard"  letters  to  construct;  do  not  fail  to  note  the 
two  horizontal  bars,  the  lower  one  being  below  the 
center  of  the  square. 

Proportions,  the  height  equals  the  width;  char- 
acteristics, the  arcs  are  the  arcs  of  ellipses,  and  the 
upper  part  of  the  letter  is  smaller  than  the  lower  part. 
The  letter  S  is  the  "hardest"  letter  to  construct,  and 
is  often  turned  backwards;  note  the  proper  "turn" 
and  that  the  upper  part  of  the  letter  is  smaller,  in  two 
directions,  than  the  lower  part. 

Proportions,  the  height  equals  the  width;  char- 
acteristics, the  two  bars  are  of  equal  length — equal  to 
the  length  of  a  side  of  the  inclosing  square — and  the 
vertical  bar,  2,  is  in  the  center  of  the  square. 

Proportions,  the  height  equals  the  width;  char- 
acteristics, the  side  lines  are  parallel  and  the  arcs  are 
arcs  of  a  circle.  Care  should  be  exercised  to  always 
make  the  letter  of  full  width,  as  the  tendency  is  to 
construct  a  letter  of  "under  width."  In  the  inclined 
letter  the  arcs  are  elliptical. 

Proportions,  the  height  equals  the  width;  char- 
acteristic, it  is  the  same  as  the  letter  A  inverted;  note 
the  full  width  at  the  top — equal  to  the  width  of  the 
square — do  not  make  it  less.  In  the  inclined  letter 
stroke  i  is  made  vertical. 

Proportions,  the  height  vqu:u»  v-  height  of 
the  square  and  the  width  is  from  one-half  to 
three- fifths  greater  than  the  height  of  the  letter 
— the  letter  W  is  the  widest  letter  in  the  alphabet; 
characteristic,  alternate  lines  are  parallel — it 
can  be  said  to  be  made  up  of  two  Vs.  The 
letter  M  is  often  inverted  for  the  letter  W;  this 
is  incorrect.  In  the  inclined  letter  strokes  i  and 
3  are  drawn  vertical. 


32 


MECHANICAL   DRAWING. 


Proportions,  the  height  equals  the  width;  char- 
acteristics, the  width  at  the  top  is  slightly  less  than 
the  width  at  the  bottom  of  the  letter  and  the  bars  cross 
above  the  center  of  the  square. 

Proportions,  the  height  equals  the  width;  char- 
acteristic, the  three  bars  unite  at  the  center  of  the 
square.  Note  that  the  full  width  of  the  square  is 
necessary  at  the  top;  do  not  make  it  less. 

Proportions,  the  height  equals  the  width;  char- 
acteristics, the  two  horizontal  bars  are  of  equal  lengths, 
and  the  diagonal,  2,  extends  from  the  upper  right- 
hand  corner  of  the  square  to  the  lower  left-hand  corner. 
The  letter  Z  is  often  made  backwards,  bar  2  being 
turned  the  wrong  way;  note  the  correct  slant. 

Proportions,  the  width  is  about  one- fourth  greater 
than  the  height;  characteristic,  it  is  the  same  as  the 
figure  8  with  the  addition  of  strokes  5  and  6. 


55.  Modifications.— The  letters  A,  C,  G,  O,  Q,  V,  and  Y 
if  made  on  the  "square"  plan  will  in  some  words  appear  to  be 
smaller  than  other  letters  similarly  constructed  and  require  to 
be  slightly  modified  to  eliminate  the  optical  illusion,  in  which 
case  the  following  is  recommended  : 

Make  the  letter  A  to  extend  slightly  above  the  other  letters 
and  to  have  a  width  at  the  bottom  a  trifle  greater  than  the  width 
of  the  side  of  the  square.  The  same  modification  is  given  for 
the  letter  V,  i.e.,  the  width  of  the  letter  should  be  greater  than 
that  of  the  other  letters,  and  it  should  extend  below  them.  The 
letters  C,  G,  O,  and  Q  may  be,  made  slightly  elliptical  in  shape, 
having  a  greater  width  than  the  side  of  the  square.  The  letter 
Y  may  be  given  increased  width  across  the  top. 

The  letters  M  and  N  are  also  susceptible  to  modification, 
though  not  for  the  same  reason  given  above.  To  construct  these 
letters  as  given  and  secure  good  results,  much  care  has  to  be 
exercised  in  drawing  the  diagonal  lines,  as  any  slight  variation 
from  the  correct  slant  is  at  once  apparent.  The  modification 


LETTERS,  FIGURES  AND  LETTERING. 


33 


PLATE  No.  3. 


\ 


\J 


34  MECHANICAL   DRAWING. 

of  these  letters  given  in  alphabet  No.  3,  Plate  No.  3,  is  recom- 
mended, being  a  style  somewhat  more  easily  constructed  and 
looks  well  if  not  quite  exact  in  all  its  lines.  Care  should  be  taken 
with  the  letter  N  not  to  make  the  diagonal  bar  too  nearly  a  hori- 
zontal line,  else  the  letter  will  become  confused  with  the 
letter  H. 

56.  Suggestions. — It  is  recommended  that  the  square  letter 
be  used  for  all  practical  and  usual  lettering,  the  modifications 
being  introduced  at  the  draughtsman's  discretion.     In  cases  where 
the  square  letter  does  not  seem  to  meet  the  requirements,  as, 
for  example,  when  it  is  desired  to  occupy  a  large  elongated  space 
with  a  few  words  or  when  it  is  required  to  place  a  large  num- 
ber of  words  in  a  comparatively  small  space,  letters  other  than 
the  square  alphabet  may  be  used  to  advantage — an  "  extended " 
letter  being  recommended  for  the  former  case  and  a  "condensed" 
type  for  the  latter  case.     (See  pages  33  (bottom)  and  181.) 

57.  Combinations  and  Spacings. — As  has  been  stated,  to  make 
printing  "stand  out"  and  be  easily  read,  it  is  first  necessary  to 
make  the  words  compact;    second,  the  spacing  must  be  uniform; 
and  third,  the  letters  must  be  of  the  same  height — be  even  along 
the  top  and  bottom.     Some  letters,  because  of  their  shape,  when 
made  and  spaced  in  the  usual  way  give  an  "open"  appearance 
to  words;    to  obviate  this  and  to  secure  compactness,  examples 
of  various  combinations  of  letters  are  given  in  Plate  No.  3;  also, 
examples  of  spacing — these  should  be  carefully  studied. 

58.  Figures. — At  the  same  time  attention  is  being  given  to 
the  upper- case  alphabet  some  study  should  be  given  to  the  pro- 
portions and  characteristics  of  figures,  since  figures  are   essen- 
tials of  drawings.     A  drawing  poorly  figured — dimensioned — is 
like  a  drawing  poorly  lettered — the  appearance  is  marred;  how- 
ever, figures  and  letters  go  hand  in  hand,  and  a  drawing  poorly 
lettered  is  usually  poorly  figured,  and  vice  versa;   a  draughtsman 
with  the  ability  to  do  good  lettering  will  usually  do  good  figures. 

Like  the  letters  the  square  type  of  figures  is  the  most  popular 
type,  the  standard  proportions  and  characteristics  being  as 
follows : 


LETTERS,  FIGURES,  AND  LETTERING. 


35 


The  figure  i  made  in  the  manner  indicated  has 
proportions,  the  height  equals  the  height  of  the  square, 
the  width  equals  the  width  of  the  line;  characteristic, 
it  is  a  simple  straight  line. 

Proportions,  the  height  equals  the  width;  character- 
istic, the  upper  portion  of  the  figure  is  larger  than  the 
lower  portion. 

Proportions,  the  height  equals  the  width;  charac- 
teristic, the  upper  portion  is  smaller  than  the  lower 
portion  of  the  figure. 

Proportions,  the  width  is  about  one-fourth  greater 
than  the  height;  characteristics,  the  short  horizontal 
stroke  at  the  top  and  the  bar  below  the  center  of  the 
square.  The  usual  tendency  is  to  make  the  figure 
of  " short  width" — it  should  be  wider  than  it  is  high; 
also,  the  stroke  3  is  often  made  too  high:  note  that  it 
is  half  way  between  the  horizontal  center  line  and 
the  bottom  of  the  square. 

Proportions,  the  height  equals  the  width;  charac- 
-  teristics,  the  upper  portion  of  the  figure  is  smaller  than 
_  the  lower  portion,  and  the  arcs  2  and  3  are  elliptical. 

Proportions,  the  height  equals  the  width;  charac- 
teristics, the  lower  portion  of  the  figure  occupies  over 
one-half  of  the  square  and  is  an  ellipse;  the  upper 
part  is  parallel  to  the  top  line  of  the  ellipse. 

Proportions,  the  height  equals  the  width;    charac- 
_  teristic,  bar  2  does  not  extend  out  on  the  left  even  with 
bar  i. 


Proportions,  the  height  equals  the  width;  charac- 
teristic, the  figure  is  made  up  of  two  ellipses,  the  upper 
ellipse  being  smaller  than  the  lower  one. 


36  MECHANICAL  DRAWING. 


Proportions,  the  height  equals  the  width;    charac- 
teristic, the  same  as  the  figure  6  inverted. 


Proportions,  the  height  equals  the  width;    charac- 
teristic, it  is  a  complete  circle,  the  same  as  the  letter  O. 


As  in  lettering,  there  is  the  vertical  and  inclined  type  of  figures, 
and  the  remarks  on  combinations  and  spacing  given  for  lettering 
obtains  for  figures  also. 

The  extended  figure — one  in  which  the  width  is  greater  than 
the  height — is  a  close  rival  of  the  square  type,  being  easily  con- 
structed and  quite  clear  in  outline.  For  some  cases  a  condensed 
figure  is  found  convenient;  it  is  well,  therefore,  for  the  student 
to  acquire  the  three  [(i)  square,  (2)  extended,  and  (3)  condensed] 
types  of  figures. 

59.  Fractions. — Examples  of  figures  arranged  into  complex 
numbers   are  given   in  Plate   No.  3,    and   should   be   carefully 
studied. 

In  mechanical  drawing  always  use  " mechanical"  figures — 
those  given  above — and  in  fractions  make  the  dividing  line  between 
the  numerator  and  the  denominator  to  be  a  straight  line  in  line 
with  the  dimension  line.  To  insure  clean-cut  fractions,  be  sure 
to  separate  the  figures  so  that  they  do  not  touch  one  another, 
particularly  do  not  permit  either  the  numerator  or  the  denomi- 
nator to  touch  the  dividing  line.  In  complex  numbers  the  whole 
number  may  be  made  from  two-thirds  to  three-fourths  of  the 
height  of  the  fraction. 

60.  Lower-case  Alphabet. — Thus  far  the  upper-case  alphabet 
has  been  discussed — figures  being  rated  as  of  the  upper  case — 
and  as  these  have  to  do  with  but  titles  and  sub- captions,  a  letter 
is  yet   to  be  adopted   for   the  notes  of   explanation  which  are 
necessary  on   drawings,  and  these    notes  usually  represent    the 
major  portion  of  the  lettering. 

For  this  work  there  are  two  very  popular  letters:  (i)  an  upper 


LETTERS,  FIGURES,  AND  LETTERING.  37 

case  alphabet  of  small  dimensions,  and  (2)  a  lower-case  alphabet, 
Fig.  15,  the  latter  being  somewhat  more  widely  in  use  because 
of  its  ease  and  rapidity  of  execution.  Of  this  letter  there  are  the 
several  styles,  square,  extended,  condensed,  vertical,  and  inclined. 

abodefghijklmnopqrstuvwxyz 
abcdefghijklmn  op  qrstuvwxyz 

Fiol5. 

The  proportions,  characteristics,  and  manner  of  construction 
may  be  studied  from  alphabet  No.  2,  Plate  No.  3.  The  general 
remarks  on  lettering,  combinations,  spacing,  etc.,  apply  to  the 
lower-case  alphabet,  and  lettering  of  this  alphabet  should  be 
made  accordingly. 

For  the  beginner  it  is  best  to  first  draw  construction  lines- 
guide  lines — in  pencil  to  block  out  the  space  for  the  letters,  or 
to  use  coordinate  ruled  paper  for  his  practice,  and  later  to  use 
only  top  and  bottom  guide  lines,  doing  the  spacing  and  pro- 
portioning "  with  the  eye. " 

61.  Mechanical  Letters. — Plate  No.  4  delineates  the  usual 
mechanical  letters — letters  made  with  instruments.  The  plain 
"block"  letter  (that  shown  in  the  top  row)  is  the  style  most  used 
and  is  the  basis  for  nearly  all  plain  and  ornamental  mechanical 
lettering.  The  plate  is  self-explanatory— adding  here  that  the 
light  construction  lines  should  not  appear  in  finished  lettering— 
and  should  be  given  due  consideration  and  study. 


MECHANICAL  DRAWING. 


PLATE  No.  4. 


CHAPTER  III. 

PROJECTION. 

62.  Scenographic  Projection. — To  project  means  to  plan,  to 
scheme,  to  delineate,  to  draw  the  outline  of  a  thing.     In  Fig.  i, 
explanatory  of  the  drawing  of  objects  viewed  from  a  finite  dis- 
tance, the  lines  joining  the  several  points  of  the  object  and  the 
point  of  sight — there  called  lines  of  sight— may  be  said  to  project 
the  image  of  the  object  on  the  retina  of  the  observer's  eye  (one  eye 
only  being  used,  since  but  one  point  of  sight  is  assumed),  and 
the  lines  themselves,  said  to  be  lines  of  projection  or  projecting 
lines.    If  these  lines  be  intersected  by  a  plane  and  the  points  in 
which  they  pierce  the  plane  be  connected  by  straight  lines,  a 
drawing  of  the  object  will  be  obtained  which  is  said  to  be  pro- 
jected onto  that  plane;    such  a  drawing — called  a  projection — 
is  an  example  of  scenographic  projection. 

If  the  intersecting  plane  be  a  plane  perpendicular  to  the 
horizontal — a  vertical  plane — the  drawing  projected  on  such  a 
plane  is  called  a  "perspective  drawing"  (Fig.  3).  For  example, 
let  the  student  station  himself  before  a  window  overlooking  a 
street  scene;  then  stretch  a  sheet  of  transparent  paper  over  the 
glass,  and  choosing  a  point  of  sight — a  view-point — look  through 
the  paper  onto  the  scene;  the  picture  will  then  seem  to  be  pro- 
jected onto  the  paper,  and  if  the  lines  be  traced  in  with  pencil 
or  ink,  the  drawing  thus  obtained  will  be  a  perspective  drawing, 
and  the  scene  said  to  be  shown  in  "  perspective." 

In  ordinary  mechanical  drawing  objects  are  but  rarely  shown 
in  scenographic  projection  or  perspective. 

63.  Orthographic    Projection. — In    mechanical    drawing,    as 
has  been  noted,  the  point  of  sight  is  assumed  as  being  at  an  infinite 

39 


40  MECHANICAL  DRAWING. 

distance  from  the  object,  and  the  lines  of  sight  to  be  practically 
parallel.  Following  the  same  line  of  reasoning  as  given  for  sceno- 
graphic  projection,  if  the  lines  of  sight  be  intersected  by  a  plane, 
and  the  points  in  which  the  lines  of  sight  pierce  this  plane  be 
joined,  a  drawing  of  the  object  will  be  obtained  which  is  said  to 
be  projected  onto  the  intersecting  plane.  If  the  intersecting  plane 
be  in  a  position  which  is  perpendicular  to  the  lines  of  sight,  the 
projection  on  that  plane  is  said  to  be  an  "orthographic  projec- 
tion," Fig.  2. 

Orthographic  projecti  n  is  the  more  useful  to  the  student 
in  engineering,  and  will  now  be  taken  up  in  detail. 

64.  The  Planes  of  Projection. — Thus  far  we  have  treated  of 
but  one  plane  of  projection — the  intersecting  plane.     To  apply 
orthographic  projection  in  mechanical  drawing,  it  is  necessary 
to  have  more  than  one  plane  of  projection,  since,  in  such  draw- 
ing, it  is  required  to  draw  more  than  one  view  of  the  object;  also, 
the  position  of  a  point,  or  object,  in  space  cannot  be  fixed,  save 
with  reference  to  the  one  plane  only  which  is  insufficient  for  the 
purpose  of  use  in  mechanical  drawing.    All  orthographic  pro- 
jection, then,  is  reckoned  with  reference  to  two  planes  of  pro- 
jection, two  planes  being  the  least  number  for  practical  work. 

The  two  planes  assumed  are  (i)  a  horizontal  plane,  called 
the  horizontal  plane  of  projection,  conventionally  designated  by 
the  letter  H,  and  called  "plane  JET,"  and  (2)  a  vertical  plane, 
called  the  vertical  plane  of  projection,  conventionally  designated 
by  the  letter  V,  and  called  "plane  F."  These  two  planes  of 
projection  are  assumed  to  be  of  infinite  expanse,  to  intersect  at 
right  angles,  and  to  divide  space  into  four  equal  parts,  called 
the  "four  quadrants." 

65.  The  Four  Quadrants.— Let   Fig.  i,  Plate  No.  5,  repre- 
sent a  limited  portion  of  each  of  the  two  planes  of  projection 
(the  drawing  shows  the  planes  to  be  of  some  thickness:    the 
planes  assumed,  however,  are  mathematical  planes  and  of  infini- 
tesimal thickness — practically  of  no  thickness),  A-B-C-D  being 
the   vertical    plane  of  projection,    V,   E-F-G-H  the   horizontal 
plane  of  projection,  H,  and  X-Y  the  line  in  which  the  two  planes 


PROJECTION. 


PLATE  No.  5. 


<u 

"o1 
CL 


_c 

Q. 


° 


O 

<D 


42  MECHANICAL  DRAWING. 

intersect,  being  the  "ground  line" — conventionally  designated 
by  the  letter  G.  With  the  planes  viewed  as  shown,  the  four 
quadrants  are  numbered  counter-clockwise,  that  in  front  of 
the  vertical  plane  and  above  the  horizontal  plane  of  projection 
being  the  first  quadrant,  that  behind  the  vertical  plane  and  above 
the  horizontal  plane  the  second  quadrant,  that  space  below  H 
and  behind  V  the  third  quadrant,  and  that  below  H  and  in 
front  of  V  the  fourth  quadrant. 

It  should  be  noted  that  the  planes  of  projection  are  viewed 
from  two  positions  only:  (i)  looking  down  as  indicated  by  the 
arrows  F,  F,  and  (2)  looking  horizontally  as  indicated  by  the 
arrows  H,  H.  With  reference  to  H  and  F,  the  projecting  lines 
used  for  projecting  points  and  lines  onto  these  planes  are 
respectively  parallel  to  these  two  directions  of  sight;  that  is,  one 
looks  vertically  down  upon  and  projects  perpendicularly  onto  the 
horizontal  plane,  and  looks  horizontally  upon  and  projects  per- 
pendicularly " against"  the  vertical  plane  of  projection. 

66.  The  Projection  of  a  Point,  with  the  Planes  V  and  H  at 
Right  Angles. — Let  P,  Fig.  i,  Plate  No.  5,  represent  a  point  in 
space;  to  find  its  horizontal  projection,  drop  the  perpendicular 
P-p  to  the  horizontal  plane,  and  the  point  pt  in  which  this  per- 
pendicular pierces  the  plane,  is  the  horizontal  projection  of  the 
point  P.  To  find  its  vertical  projection,  erect  the  perpendicular 
P-pf  to  the  vertical  plane,  and  the  point  /,  in  which  this  per- 
pendicular pierces  F,  is  the  vertical  projection  of  the  point  P. 
These  two  projections,  p  and  pf,  fix  the  position  of  the  point  P 
with  reference  to  the  planes  F  and  H;  for,  given  p  and  /,  by 
erecting  perpendiculars  to  the  planes  F  and  H,  the  two  per- 
pendiculars will  intersect  at  P  and  thus  define  the  position  of 
the  point. 

The  student  should  also  note  that  the  perpendicular  P-p  to 
the  plane  H  shows  on  the  vertical  plane  as  the  line  p'-o,  for 
to  obtain  the  projection  of  a  straight  line  it  is  but  necessary  to 
project  any  two  points  of  the  line  and  join  their  projections.  In 
this  case  the  two  points  taken  are  the  two  extremes,  P  and  p 
(this  is  the  usual  method  of  projecting  a  definite  portion  of  a 


PROJECTION.  43 

line),  /  being  the  vertical  projection  of  P,  and  o  the  vertical  pro- 
jection of  p\  also,  the  horizontal  projection  of  the  projecting  line 
P-p'  is  p-o.  It  is  obvious  that  p-o  and  pf-o  are  perpendicular 
to  each  other,  being  adjacent  sides  of  the  rectangle  P-p-o-p' '. 

67.  The  Planes  V  and  H  Revolved. — If  compelled   to   con- 
struct all  projections  with  the  planes  V  and  H  in  their  true  posi- 
tions— F,  vertical,  and  H,  horizontal — the  task  would  be  entirely 
too  laborious  and  time-consuming  for  practical  use.     That  the  art 
may  become  practical,  the  vertical  plane  is  assumed  to  be  revolved 
into  coincidence  with  the  horizontal  plane,  thus  forming  but  one 
plane ;  and  assuming  the  plane  of  the  paper  to  be  a  limited  portion 
of  this  plane,  the  problem  is  solved. 

Explanatory. — Plate  No.  5.  Let  Fig.  i  represent  a  limited 
portion  of  the  planes  V  and  H,  and  let  the  plane  V  (A-B-C-D)  be 
revolved  in  the  direction  of  the  arrows  (counter-clockwise)  until 
it  becomes  coincident  with  the  plane  H  (E-F-G-H).  Fig.  2 
represents  an  intermediate  position  of  V  in  its  revolution,  and 
Fig.  3  the  coincident  position.  Now,  assume  the  planes  as 
depicted  in  Fig.  3  to  be  picked  up  and  " squared  about,"  pre- 
senting themselves  as  shown  in  Fig.  4.  Considering  the  first 
quadrant,  it  will  be  noted  that  the  vertical  plane  falls  above  the 
ground  line  and  that  the  horizontal  plane  falls  below  the  ground 
line.  The  first  quadrant,  only,  is  considered  in  the  following  dis- 
cussion. 

[To  facilitate  his  conception  of  the  following  projections,  the 
student  is  advised  to  construct  a  pasteboard  or  wooden  model  of 
the  planes  V  and  H,  capable  of  being  revolved.  Take  two  pieces 
of  pasteboard  about  six  or  eight  inches  square,  cut  a  straight  slot 
half  way  across  the  middle  of  each  and  put  the  two  pieces  together, 
slot  to  slot,  and  press  "home";  this  will  give  a  model  which 
revolves  into  one  plane,  approximately.] 

68.  The  Conventional  Projection  of  a  Point. — Plate   No.  5. 
Referring  again  to  Fig.  i  depicting  the  projection  of  the  point  P, 
it  is  obvious  that  the  figure  P-p-o-{/  is  a  rectangle  whose  plane  is 
both  perpendicular  to  the  planes  V  and  H,  and  to  their  inter- 
section, X-Y.    Now  as  the  planes  of  projection  are  revolved  intc 


44  MECHANICAL  DRAWING. 

coincidence,  note  the  revolution  of  the  projections  of  the  point  P 
(Figs.  2,  3,  and  4)  and  it  is  seen  that  the  two  projections  are  in  the 
same  straight  line  perpendicular  to  the  ground  line.  The  student 
should  also  note  that  the  distance  of  the  point  P  from  the  vertical 
plane  is  shown  on  the  horizontal  plane  by  the  perpendicular 
p-o]  also,  that  the  distance  of  the  point  P  from  the  horizontal 
plane  is  shown  on  the  vertical  plane  by  the  perpendicular  p'-o\ 
from  which  we  deduce,  the  distance  of  a  point  from  the  vertical 
plane  of  projection  is  measured  on  the  horizontal  plane,  and  the 
distance  of  a  point  from  the  horizontal  plane  of  projection  is 
measured  on  the  vertical  plane. 

As  has  been  stated,  the  planes  V  and  H  are  assumed  to  be 
of  infinite  expanse,  and  instead  of  considering  definite  portions 
of  these  planes,  as  has  been  done  thus  far,  for  practical  work  the 
planes  are  assumed  by  simply  drawing  the  ground  line  X-Y,  and 
when  considering  the  first  quadrant  only — as  is  here  done — 
understanding  that  all  the  space  above  X-Y  represents  the  vertical 
plane,  F,  and  all  of  the  space  below  X-Y  represents  the  hori- 
zontal plane,  H.  The  conventional  projection  of  the  point  Py 
then,  is  shown  by  Fig.  5. 

69.  The  Conventional  Assumption  of  a  Point. — Plate  No.  5. 
A  point  is  assumed  by  its  two  projections  (one  projection  does 
not  fix  the  position  of  the  point,  two  are  necessary);  also,  these 
two  projections  always  lie  in  the  same  straight  line,  perpendicular 
to  the  ground  line. 

Let  it  be  required  to  assume  a  point  P,  four  inches  from  the 
vertical  plane  of  projection,  and  ten  inches  from  the  horizontal 
plane.  (Fig.  5.)  First  draw  the  ground  line  X-Y  (the  ground 
line  is  always  drawn  as  a  horizontal  line)  and  erect  the  indefinite 
perpendicular  p-o-p';  now,  since  the  distance  of  a  point  from 
the  plane  V  is  measured  on  H,  lay  off,  from  the  ground  line,  a 
length  o-p,  equal  to  four  inches— the  distance  of  the  given  point 
from  F— and  the  extremity,  p,  of  this  length  represents  the  hori- 
zontal projection  of  the  point.  In  like  manner,  to  obtain  the 
vertical  projection  of  the  point,  lay  off,  from  the  ground  line,  a 
length  o-p',  equal  to  ten  inches — the  distance  of  the  point  from 


PROJECTION.  45 

the  horizontal  plane — and  the  extremity,  f/y  of  this  length  repre- 
sents the  vertical  projection. 

The  student  should  make  it  a  point  to  clearly  understand 
all  points  connected  with  the  assumption  and  projection  of  a 
point  before  going  farther,  as  a  clear  understanding  of  all  subse- 
quent projections  is  dependent  upon  a  clear  conception  of  the 
projection  of  a  point. 

Corollary. — From  the  foregoing  it  is  obvious  that  the  vertical 
projection  of  a  point  which  lies  in  the  horizontal  plane  is  in  the 
ground  line,  as  the  vertical  projection  of  the  point  p,  Fig.  5,  is 
o,  a  point  in  X-Y ;  also,  that  point  //,  in  the  vertical  plane,  is 
horizontally  projected  in  (o)  the  ground  line. 

70.  The  Projection  of  a  Straight  Line. —  Plate  No.  5.    To 
obtain  the  projection  of  a  straight  line,  it  is  necessary  to  project 
but  two  (any  two)  points  of  the  line,  and  then  join  the  projections 
with  a  straight  line.    Let  M-N,  Fig.  6,  be  a  line  in  space;   the 
two  points  projected  are  the  two  extremes  of  the  line,  M  and  N 
(this  being  the  usual  practice  when  dealing  with  a  line  of  defi- 
nite length),  M  being  horizontally  projected  at  m,  N  horizon- 
tally projected   at  n,  and  m-n  the  horizontal  projection  of  the 
line.    It  is  obvious  that  m'-nr  represents  the  vertical  projection 
of  the  line.    Fig.   7  represents  the  conventional  projection  of 
M-N. 

Corollary. — It  is  evident  from  the  foregoing  that  the  projection 
of  curved  lines  is  obtained  in  a  similar  manner,  that  is,  by  pro- 
jecting a  number  of  points  of  the  curves,  and  joining  the  pro- 
jections of  these  points  by  curved  lines. 

71.  The  Projection  of  a  Line  which  is  Parallel  to  One  of  the 
Planes  of  Projection. — Plate  No.  6.     Let  Fig.   i  represent  the 
projection  of  a  line  M-N  which  is  parallel  to  the  horizontal  plane 
of  projection,  m-n  being  its  horizontal  projection,  and  m'-nf  its 
vertical  projection.     Since  the  line  is  parallel  to  H,  all  of  its  points 
are  at  the  same  distance  from   the  horizontal  plane,  hence  the 
vertical  projection  is  parallel  to  the  ground  line — the  distance  from 
H  being  measured  on  V\    also,  since  in  the  figure  M-N-n-m 
M-m  equals  N-n,  and  the  angles  M-m-n  and  N-n-m  are  right 


46  MECHANICAL  DRAWING. 

angles,  the  figure  is  a  rectangle  and  M-N  is  parallel  and  equal  to 
m-n.     Therefore: 

A  line  which  is  parallel  to  one  of  the  planes  of  projection  has 
for  its  projection  on  that  plane  a  parallel  line  of  equal  length,  and 
for  its  other  projection  a  line  which  is  parallel  to  the  ground 
line.  (A  line  is  projected  in  its  true  length  only  on  a  parallel 
plane.) 

Fig.  2  is  the  conventional  method  of  drawing  the  above  pro- 
jection. 

72.  To  Find  the  True  Length  of  a  Line.— Plate  No.  6.  Having 
demonstrated  that  a  line  is  projected  in  its  true  length  on  a  parallel 
plane,  it  is  obvious  that,  to  show  the  true  length  of  a  line  which 
is  oblique  to  the  planes  V  and  H,  it  is  necessary  to  revolve  it 
about  some  point  as  an  axis — usually  one  extreme  if  a  definite 
line — until  it  becomes  parallel  to  one  of  the  planes  of  projection, 
when  it  will  be  projected  on  that  plane  in  its  true  length. 

Let  M-N,  Fig.  4,  represent  a  line  in  space  which  is  oblique  to 
both  V  and  H,  and  let  it  be  required  to  find  the  true  length  of 
the  line  by  revolving  it  parallel  to  the  vertical  plane  of  projection. 
In  the  revolution,  it  must  be  understood,  the  position  of  all  of 
the  points  of  M-N  are  unaltered  with  respect  to  plane  H;  that  is, 
if  the  point  M ,  for  example,  be  three  inches  from  H  in  its  original 
position,  the  point  M  must  be  three  inches  from  H  in  the  revolved 
position:  the  position  of  the  line  is  altered  with  respect  to  V, 
only.  Let  the  line  be  revolved,  in  accordance  with  the  above, 
from  the  original  position,  M-N,  about  N  as  an  axis,  until  it 
occupies  a  position  M"-N,  parallel  to  V,  when  its  projections  are 
m"-n  on  the  horizontal  plane  (note  that  this  projection  is  parallel 
to  the  ground  line)  and  m'"-ri  on  the  vertical  plane  of  projection; 
the  line  m'"-n',  then,  represents  the  true  length  of  M-N. 

The  conventional  procedure  is  illustrated  by  Fig.  3.  The  line 
M-N  is  assumed  by  its  two  projections  m-n  and  mf-n',  the  hori- 
zontal and  vertical  projections  respectively.  To  find  the  true 
length  by  revolving  into  parallelism  with  the  vertical  plane,  with 
the  point  n  as  a  center  and  a  radius  n- m  describe  the  arc  m-m" ; 
now,  since  the  distance  of  the  point  m  is  unchanged  with  reference 


PROJECTION. 


47 


PLATE  No.  6. 


. 


*    1 


u 

!* 

"o 

O> 
Q. 
V) 


V 


48  MECHANICAL  DRAWING. 

to  the  horizontal  plane,  the  vertical  projection  of  the  arc  m-m'r 
is  the  straight  line  m'-m"f ,  parallel  to  the  ground  line.  The 
point  n,  being  used  as  a  center  of  revolution,  remains  fixed,  hence 
its  vertical  projection  remains  unchanged  and  the  vertical  pro- 
jection of  the  revolved  line  is  m'"-n ',  the  true  length  of  the 
line. 

73.  The  Projection  of  a  Straight  Line  which  is  Perpendicular 
to  one  of  the  Planes  of  Projection. — Plate  No.  6.     Let  M-N9 
Fig.  5,  represent  a  line  in  space  which  is  perpendicular  to  the 
horizontal  plane;    it  is  obvious  that  all  of  its  points  are  horizon- 
tally projected  in  the  same  point,  and  that  the  projection  of 
the  line  on  H  is  simply  a  point,  while  its  vertical  projection  is 
a  line  m'-n',  perpendicular  to  the  ground  line;    therefore,  aline 
which  is  perpendicular  to  one  of    the  planes  of  projection  is 
projected  on  that  plane  as  a  point,  while  its  other  projection 
is  a  straight  perpendicular  line  to  the  ground  line;   the  conven- 
tional projection  is  shown  in  Fig.  6. 

74.  The   Assumption   of   Planes. — Plate    No.    6.       A    point 
and  a  line  are  assumed  by  their  two  projections;  a  plane  is  assumed 
by  its  "traces."     In  Fig.  5  the  triangle  t-T-tf  represents  a  por- 
tion of  a  plane  which  is  oblique  to  the  planes  of  projection;  the 
line  t-T  represents  the  intersection  of  the  given  plane — conven- 
tionally designated  by  the  letter  71,  and  called  plane  T — with 
plane  H,  and  the  line  T-f  represents  the  intersection  of  T  with  V. 
These  lines  of  intersection  are  called  the  " traces"  of  the  plane. 
It  is  obvious  that  the  traces  of  a:  given  plane,  as  plane  T,  inter- 
sect in  the  ground  line;  also,  that  when  the  traces  of  a  plane  are 
once  assumed,  the  position  of  the  plane  becomes  fixed;   hence  a 
plane  is  assumed  by  its  traces. 

Fig.  5  illustrates,  also,  the  projection  of  a  point  P  which  is 
in  the  plane  T,  the  projections  p  and  f/  being  obtained  by  drop- 
ping perpendiculars  to  If  and  V  respectively. 

Fig.  6  depicts  the  conventional  method  of  assuming  plane  T1, 
and  the  projection  of  point  P  in  the  plane. 

The  student  is  advised  to  provide  himself  with  two  paste- 
board planes  (one  piece  to  be  cut  in  the  shape  of  a  rhombus 


PROJECTION.  49 

and  the  other  to  be  rectangular)  to  facilitate  his  conception  of 
the  following  remarks: 

Fig.  8  is  a  drawing  illustrating  (i)  a  plane  which  is  perpen- 
dicular to  H  and  oblique  to  F,  (2)  a  plane  which  is  perpendicular 
to  V  and  oblique  to  H,  and  (3)  a  plane  which  is  perpendicular 
to  both  H  and  V.  The  student  should  note  that  the  vertical 
trace  of  i  is  perpendicular  to  the  ground  line,  G,  that  the  hori- 
zontal trace  of  2  is  perpendicular  to  the  ground  line,  and  that 
both  traces  of  3  are  perpendicular  to  the  ground  line.  Fig.  7  is 
the  conventional  method  of  representing  the  above  planes. 

In  3,  Fig.  8,  let  P  represent  a  point  in  the  plane;  also,  let  A-B 
represent  a  plane  figure  in  the  plane;  it  is  obvious  that  all  such 
points,  lines,  and  figures  within  the  plane  are  projected  in  the 
traces  of  the  plane — the  line  #'-£>',  for  example,  represents  the 
vertical  projection  of  the  closed  curve  A-B. 

As  a  further  exposition  of  the  subject,  and  to  demonstrate  its 
practical  use  in  mechanical  drawing,  the  following  representa- 
tive problems  in  projection  are  elucidated : 

75.  PROBLEM  i.  To  Draw  the  Projections  of  a  Hollow  Cube 
when  in  Three  Different  Positions. — Plate  No.  7.  Let  the  first 
position  be  with  all  of  its  faces  either  parallel  or  perpendicular  to 
the  planes  of  projection,  as  i,  Fig.  i.  Now,  as  a  point  is  assumed 
by  its  two  projections,  so  is  an  object  assumed  by  its  two  pro- 
jections; hence,  to  assume  the  cube,  draw  i,  Fig.  3,  which  is  the 
horizontal  projection — the  same  as  a  plan  of  the  cube, — then 
draw  2,  the  vertical  projection — the  same  as  an  elevation — of 
the  cube.  The  projections  are  drawn  in  this  order,  that  the 
hole  through  the  cube  may  be  projected  from  i  to  2,  in  which 
it  is  indicated  by  dashed  lines.  These  two  projections  drawn, 
the  object  is  assumed  in  its  first  position. 

For  the  second  position  of  the  cube,  let  it  be  assumed  to  be 
revolved,  about  a  vertical  axis  through  its  center,  through  an 
angle  of  45°,  without  altering  its  position  with  respect  to  the 
horizontal  plane;  that  is,  the  cube  does  not  move  either  up  or 
down  along  the  axis  of  revolution;  2,  Fig.  i,  illustrates  this  new 
position  of  the  cube.  3,  Fig.  3,  represents  the  conventional 


PLATE  No.  7. 


MECHANICAL  DRAWING. 


PROJECTION.  51 

horizontal  projection  (plan)  of  the  cube  when  revolved;  to  find 
its  vertical  projection,  number  all  of  the  corners  of  the  cube, 
when  the  problem  becomes  the  projection  of  points,  for,  since 
the  position  of  the  cube  remains  unchanged  with  respect  to  the 
horizontal  plane,  the  height  of  the  projection  of  the  various  points 
on  the  vertical  plane  remains  unchanged,  and  as  the  two  pro- 
jections of  a  point  are  always  in  the  same  perpendicular  to  the 
ground  line,  the  vertical  projection  of  the  points  may  be  obtained 
by  projecting  horizontally  from  2  and  vertically  from  3,  when 
it  is  evident  that  the  intersection  of  the  projections  from  the  like 
numbered  point  will  be  the  new  position  of  that  point — its  ver- 
tical projection.  Having  projected  all  of  the  points,  join  them  by 
straight  lines,  and  the  vertical  projection  of  the  revolved  cube  is 
obtained. 

For  the  third  position  of  the  cube,  let  its  position  be  altered 
with  reference  to  the  horizontal  plane  only;  this  is  done  by  assum- 
ing the  point  numbered  8  to  remain  fixed,  then  revolving  the 
object  about  this  point  through  an  angle  of  30°.  3,  Fig.  i, 
shows  the  cube  when  in  this  last  position,  and  5,  Fig.  3,  repre- 
sents its  conventional  vertical  projection.  To  obtain  the  hori- 
zontal projection,  since  the  position  of  the  points  are  not  changed 
with  reference  to  F,  and  since  the  two  projections  of  a  point  must 
lie  in  the  same  perpendicular  to  the  ground  line,  project  horizon- 
tally from  3  and  vertically  from  5,  and  the  drawing  numbered  6 — 
the  horizontal  projection  of  the  cube  when  in  its  third  portion — 
is  obtained. 

REMARKS. — Drawings  i  and  2,  Fig.  ,3,  are  original  projections; 
drawing  3  is  a  copy  of  drawing  i,  turned  through  an  angle  of  45°; 
4  is  a  projection;  5  is  a  copy  of  4,  tilted  30°;  and  drawing  6  is  a 
projection. 

76.  Problem  2.  To  Draw  the  Projections  of  a  Hexagonal  Nut 
when  in  Two  Different  Positions. — Let  the  first  position  of  the 
nut  be  when  the  plane  of  its  base  is  parallel  to  the  vertical  plane 
of  projection,  as  shown  by  position  i,  Fig.  17.  To  draw  the 
conventional  projection  of  the  nut  when  in  this  position,  draw  i, 
Fig.  18,  the  vertical  projection,  or  elevation,  of  the  nut,  then 


MECHANICAL   DRAWING. 


project  2,  the  horizontal  projection,  or  plan,  of  the  nut  (the  draw- 
ings are  constructed  in  this  order,  that  the  corners  of  the  hexagon 


V 

may  be  projected  from  i  to  2);  these  two  drawings  complete, 
the  object  is  then  assumed  (by  its  projections)  in  its  original 
position. 


PROJECTION.  53 

As  a  second  position,  let  the  position  of  the  nut  be  changed 
with  reference  to  the  vertical  plane  only,  by  changing  its  position 
from  the  parallel  one  to  one  of  30°  with  the  vertical  plane,  as 
shown  by  position  2,  Fig.  16.  To  obtain  the  conventional  pro- 
jection of  the  nut  when  in  this  position,  draw  3,  Fig.  18,  its  hori- 
zontal projection  (which  is  a  copy  of  2,  turned  30°  to  the  ground 
line);  then  to  draw  its  vertical  projection  proceed  as  follows: 

To  find  the  projection  of -the  outline  of  the  nut,  number  all 
of  the  corners,  that  is,  number  every  point  of  i  and  2  (the  same 
point  having  the  same  number  in  all  of  its  projections)  and  trans- 
fer the  numbering  of  2  to  3,  when,  by  projecting  vertically  from 
3  and  horizontally  from  i,  the  fourth  position  of  the  points  is 
defined  by  the  intersection  of  the  projections  from  correspond- 
ingly numbered  points;  these  points  being  then  joined  by  straight 
lines  give  the  vertical  projection  of  the  straight  lines  of  the  object. 
For  the  curved  lines  of  the  object,  a  number  of  points  in  each 
curve  must  be  projected  and  their  projections  joined  by  curved 
lines.  For  example,  take  the  curved  edges  of  the  front  face  of 
the  nut;  three  points  will  be  necessary,  the  two  extremes  and 
the  middle  point;  this  latter  point  is  indicated  by  the  figure  3  in 
Fig.  1 8,  and  the  method  of  its  pf ejection  shown. 

To  project  the  circles  showing  on  the  front  face  of  the  nut, 
each  circle  should  be  divided  into  a  number  of  points  (twelve 
points,  equally  spaced,  being  a  good  working  number),  these 
points  numbered,  and  then  carried  through  the  four  drawings. 
(The  point  numbered  2  on  the  large  circle,  and  the  point  num- 
bered i  on  the  small  circle  illustrate  the  method  of  procedure.) 
To  obtain  that  portion  of  the  small  circle  showing  at  the  rear  of 
the  nut — the  position  of  the  nut  being  such  that  the  observer  can 
see  through  it, — the  projection  of  the  points  of  the  small  circle 
in  i  are  projected  onto  the  rear  of  2  (the  line  nearest  the  ground 
line),  then  copied  on  the  rear  of  3,  and  from  there  projected  verti- 
cally to  intersect  with  the  horizontal  projections  from  the  same 
points  of  i ;  the  intersections  are  then  connected  by  a  curved  line. 
Observe  that  the  projections  of  the  circles  of  i  show  as  straight 
lines  in  2  and  3,  the  straight -line  projections  being  because  the 


54  MECHANICAL  DRAWING. 

plane  of  the  circles  is  perpendicular  to  the  horizontal  plane; 
also  note  that,  for  a  similar  reason,  two  of  the  curved  sides  of 
the  front  face  of  the  nut  project  in  4  as  straight  lines,  the  plane 
of  each  curve  being  perpendicular  to  V. 

77.  PROBLEM  3. —  The  Projection  of  a  Small  Hand-wheel. 
This  projection  is  given  to  illustrate  the  application  of  the  fore- 
going principles  to  ordinary  mechanical  drawing.  Let  the  hand- 
wheel  to  be  projected  be  such  a  one  as  is  illustrated  by  Fig.  19. 
Now,  suppose  one  has  a  front  elevation  of  a  machine  drawn,  in 
which  the  hand- wheel  shows  on  the  right  side  as  the  rectangle 
D-$-$-B  (A,  Fig.  20),  at  45°  to  the  horizontal,  and  is  required 
to  draw  the  right  side  elevation  of  the  machine,  necessitating  the 
projecting  of  the  hand- wheel  to  this  new  position. 

To  Project  the  Rim. — First,  draw  the  full  section  of  the 
wheel  within  the  elevation — a  sectional  elevation — as  is  indicated 
by  the  dashed  lines  in  A,  Fig.  20,  then  on  the  front  line  of  the 
elevation,  D-$,  as  a  center-line,  lay  out  one-half  of  a  "square 
view"  of  the  wheel,  as  indicated  by  the  dotted  portion  of  the 
drawing.  Next  let  the  vertical  center  line,  5-5  (B),  represent  the 
position  of  the  center 'line  for  the  hand-wheel  in  the  side  eleva- 
tion drawing,  and  at  some  point  along  it— preferably  some  dis- 
tance above  a  horizontal  line  through  the  top  point,  5,  of  A,  or 
just  below  a  horizontal  line  drawn  through  the  bottom  point,  D, 
of  A — construct  a  similar  drawing  to  the  dotted  portion  of  A] 
the  projection  may  now  be  begun. 

In  Fig.  20  the  projected  figure  is  but  half  complete,  being 
an  amount  sufficient  to  illustrate  the  method  of  procedure;  the 
dotted-half  views  are,  however,  all  that  is  required  to  construct 
a  finished  projection. 

In  such  a  projection  as  the  one  in  hand  it  is  best  to  consider 
but  one  "feature"  of  the  object  at  a  time,  and  to  complete  the 
projection  of  this  one  feature  before  taking  up  a  second  one, 
thus  minimizing  possible  confusion.  With  this  suggestion  in 
mind,  divide  the  hand- wheel  into  the  hub,  the  rim,  and  the  arms, 
and  first  consider  the  projection  of  the  outside  of  the  front  face  of 
the  rim — the  straight  line  $-D  of  the  A  elevation,  shown  also  as 


PROJECTION. 


55 


the  dotted  circle  $-D  of  the  same  figure.     To  project  this  circle, 
first  divide  it  into  a  number  of  points,  as  5,  4,  3,  i,  then  project 


'•  |''1|l'  v'     /  ,'X  /       \ 

-  -  i*'  -^      '  ^-^ 

M-fe/'x-X     \ 


these  points,  perpendicularly,  onto  the  straight  line  $-D,  and 
number  them  that  they  may  be  easily  followed.     Next,  locate  the 


56  MECHANICAL  DRAWING. 

outside  circle  of  the  dotted  drawing  of  B,  and  divide  it  into  a 
number  of  arcs,  equal  to  those  of  the  same  circle  in  A ,  and  number 
each  point  to  correspond  with  the  same  point  in  A.  Since  the 
projected  view  is  at  right  angles  with  the  original  position  of 
the  wheel,  it  is  evident  that  the  extreme  point  5  of  A  is  the 
center  point  5  of  B,  and  that  the  center  point  i  of  A  constitutes 
the  two  extremes  of  B,  a  fact  which  renders  the  numbering  of 
the  other  points  an  easy  matter.  In  the  drawing,  the  circles  are 
divided  into  a  number  of  equal  arcs  corresponding  to  twelve 
equal  divisions  in  a  complete  circumference:  this  is  in  accordance 
with  the  usual  practice,  which  is  to  divide  the  circumference  into 
an  equal  number  of  equal  arcs,  for  when  thus  divided  a  circle 
presents  duplicate  divisions  when  viewed  from  first  one  position, 
and  then  from  a  position  at  right  angles  to  the  first  one.  With 
the  points  in  each  drawing  properly  numbered,  project  vertically 
from  B  and  horizontally  from  A,  and  the  intersection  of  the 
projections  from  the  same  numbered  point  will  be  the  new  posi- 
tion of  that  point;  the  points  being  then  joined  by  a  smooth 
curved  line,  give  the  side  view  of  the  outside  of  the  front  face  of 
the  rim. 

Next,  consider  the  projection  of  the  inside  line  of  the  front 
face  of  the  rim — the  dotted  circles  9-8-7-6 — and  proceeding  by 
projecting  a  number  of  its  points  as  explained  above,  the  curve 
6-7-8-9,  etc.,  of  B  is  obtained — the  side  view  of  the  inside  of  the 
front  face  of  the  rim. 

The  inside  and  outside  lines  of  the  front  face  of  the  hub  of 
the  wheel  are  projected  in  the  same  manner  as  directed  for  the 
lines  of  the  rim. 

Now  let  the  arrows  sy  s,  s  represent  lines  of  sight  directed 
against  the  front  elevation  A,  the  point  of  sight  being  at  an  infinite 
distance  to  the  right;  and  having  the  figure  well  in  mind,  con- 
sider just  what  lines  of  the  front  elevation  will  be  visible  in  the 
side  view.  Referring  to  the  rim,  it  is  evident  that  the  outside 
and  inside  lines  of  its  rear  face  will  appear  at  top  and  bottom, 
respectively,  in  the  side  elevation,  the  method  of  projection  being 
clearly  shown  in  the  drawing.  It  is  also  evident  that  the  outside 


PROJECTION.  57 

line  of  the  rear  face  of  the  hub  will  be  partly  visible  in  the  side 
view. 

To  Project  the  Arms. — From  a  previous  explanation,  it  is 
evident  that  the  center  arm — that  shown  as  a  rectangle  in  A— 
will  be  shown  as  horizontal  in  B,  extending  to  the  extremes, 
right  and  left,  and  that  the  other  two  arms  of  A — the  two  extending 
to  the  extremes,  top  and  bottom — will  show  on  the  vertical  center 
line  of  B.  First  consider  the  upper  arm  of  A,  an  inspection  of 
which  shows  three  points  to  project;  X,  the  intersection  of  the 
center  line  of  its  front  face  with  the  hub,  and  Y,  the  intersection 
of  its  side  face  with  the  hub.  (Note  the  projection  of  these 
points  from  the  dotted  drawing  of  A  to  the  front  line  of  the 
sectional  elevation  of  the  arm.)  By  projecting  horizontally  from 
these  points  to  an  intersection  with  the  vertical  projection  from  the 
dotted  position  of  the  same  points  in  B,  three  points  are  obtained 
— one  central  point  and  two  extremes — through  which  the  full- 
line  curve  Y-X-Y,  representing  the  intersection  of  the  arm  with 
the  hub,  may  be  drawn,  and  the  points  Y,  Y  being  established, 
the  projection  of  the  arm  is  completed  by  drawing  vertically  from 
these  points  to  the  inside  line  of  the  front  face  of  the  rim,  the 
intersection  of  the  arm  with  the  rim  being  hidden.  It  is  obvious 
that  the  curve  of  intersection,  Y-X-Y,  of  the  arm  and  hub  is 
parallel  to  the  same  portion  of  the  outside  line  of  the  hub. 

To  project  the  horizontal  arms  of  B,  it  is  evident,  from  an 
inspection  of  the  sectional  elevation,  that  there  are  two  sides  or 
faces — the  top  and  front — to  project,  the  work  being  clearly 
shown  by  the  drawing. 

It  will  have  been  observed  that,  because  of  the  even  number 
of  arms  in  the  hand-wheel,  the  drawings  become  symmetrical, 
and  a  number  of  the  points  project  simultaneously.  If  the  hand- 
wheel  had  an  uneven  number  of  arms,  say  five,  the  dotted  half 
views  would  have  to  be  complete  views,  and  each  arm  projected 
separately,  the  circles  being  projected  as  explained. 

78.  PROBLEM  4. — Projections  of  a  Frustum  of  a  Hexagonal 
Right  Pyramid  and  its  Development.  —  Let  the  pyramid  be 
assumed  as  resting  on  the  horizontal  plane,  and  let  its  position 


58  MECHANICAL  DRAWING. 

with  reference  to  the  vertical  plane  be  such  as  is  defined  by  the 
drawings  i  and  2,  Fig.  22 — its  horizontal  and  vertical  projection 
respectively.  The  pyramid  is  first  assumed  as  a  whole,  the 

The  Orthographic  Projection  of  the  frustum  of  a  pyramid. 


The  Pyramid.. 


FIG.  21. 

"frustum"  not,  as  yet,  entering  into  the  problem.  The  draw- 
ings are  constructed  in  the  order  numbered,  that  the  edges  of  2 
may  be  projected  from  i.  Now  that  the  pyramid  is  fixed,  let 


FIG.  22. 

the  upper  base  of  the  frustum  be  formed  by  cutting  the  pyramid 
with  a  plane,  T,  which  is  perpendicular  to  V  and  at  30°  with  H, 
and  let  the  cutting  plane  intersect  the  vertical  center  line  of  the 


PROJECTION.  59 

pyramid  at  a  point  one  inch  above  its  base.  The  plane  of  the 
upper  base  of  the  frustum  is,  of  course,  in  the  cutting  plane,  and 
this  being  perpendicular  to  F,  the  plane  of  the  base  is  perpen- 
dicular to  F,  and  is  there  projected  as  the  straight  line  7-10,  one 
inch  up  the  center  line  and  at  30°  with  the  horizontal,  as  shown  in 
2.  The  frustum  is  now  assumed,  but  the  upper  base  shown  only 
in  its  vertical  projection.  Now  to  obtain  its  horizontal  projec- 
tion : 

The  pyramid  has  six  edges,  and  each  edge  has  a  point  of 
intersection  with  the  upper  base;  that  is,  to  form  the  upper  base, 
«ach  edge  has  been  cut  by  a  plane.  Now,  each  edge  is  shown 
in  its  two  projections,  and  since  the  points  of  intersection  of 
the  edges  with  the  plane  of  the  upper  base  must  be  horizontally 
projected  in  some  point  on  the  horizontal  projection  of  the  edges, 
and  since  the  projections  of  a  point  are  always  in  the  same  perpen- 
dicular to  the  ground  line,  it  is  evident  that  the  horizontal  pro- 
jection of  the  points  of  intersection  of  the  edges  with  the  upper 
base  is  the  intersection  of  the  projection  from  the  vertical  inter- 
sections with  the  horizontal  projection.  For  example,  consider 
the  point  12  of  2:  12  is  on  the  edge  6-0;  the  horizontal  projection 
of  this  edge  is  the  line  6-0  of  i ;  the  horizontal  projection  of  the 
point  must  be  on  the  line  6-0  (i)  and  must  lie  in  the  perpendicular 
through  12  (2)  to  the  ground  line;  therefore  the  horizontal  pro- 
jection of  the  point  is  the  intersection  of  6-0  (i)  and  the  per- 
pendicular 12-12.  The  other  five  points  of  the  upper  base  are 
projected  from  the  vertical  to  the  horizontal  in  a  similar  manner, 
and  these  points  being  joined  by  straight  lines,  as  indicated  in 
the  drawing,  represent  the  horizontal  projection  of  the  upper 
base. 

Let  it  be  now  required  to  show  the  true  size  of  the  upper 
base  of  the  frustum.  It  is  obvious  that  since  the  plane  of  this 
base  is  at  an  angle  with  H,  the  projected  base  in  i  does  not  repre- 
sent the  true  size  of  the  base.  To  show  the  true  size,  the  base 
must  be  projected  onto  a  plane  which  is  parallel  to  it.  In  draw- 
ing 4,  let  the  line  7-10,  parallel  to  7-10  of  2,  represent  such  a  plane; 
the  projection  is  then  made  on  this  plane,  and  to  "show"  it,  the 


60  MECHANICAL  DRAWING. 

plane  is  revolved  into  the  vertical  plane  of  projection,  the  prac- 
tical solution  being  as  follows: 

Draw  the  line  7-10  (4)  parallel  to  and  at  an  optional  distance 
from  the  line  7-10  (2),  then  draw  the  indefinite  perpendiculars 
7-7,  8-8,  etc.  It  is  obvious  that  the  true  length  of  the  base  is 
defined  by  the  intersections  of  the  perpendiculars  7-7  and  10-10 
with  the  line  7-10  (4).  The  true  widths  of  the  base  are  shown 
in  its  horizontal  projection  (i),  for  it  is  evident,  since  the  plane 
of  the  base  is  perpendicular  to  F,  a  straight  line  joining  the  points 
8  and  12,  for  example,  is  parallel  to  H,  and  being  parallel,  will 
there  be  projected  in  its  true  length.  Combining  these  "true 
widths"  with  the  "true  lengths"  of  drawing  4 — using  the  line 
7-10  as  a  center  line — a  drawing  representing  the  true  size  of 
the  upper  base  of  the  frustum  is  obtained. 

Let  the  frustum  now  be  tilted  on  the  point  4  of  the  lower 
base,  until  the  plane  of  this  base  is  in  a  position  30°  with 
the  horizontal  plane,  without  changing  its  position  with  refer- 
ence to  F,  and  let  it  be  required  to  draw  the  H  and  F  projec- 
tions. 

To  draw  the  F  projection,  copy  drawing  2,  tilted  to  30°  with 
the  ground  line,  as  drawing  5,  B.  Now,  since  the  position  of 
the  frustum  with  reference  to  F  has  not  been  changed,  and  since 
the  two  projections  of  a  point  must  lie  in  the  same  perpendicular 
to  G,  the  H  projection  is  obtained  by  projecting  horizontally 
from  i,  A,  and  vertically  from  5,  B.  This  will  give  a  complete 
projection — upper  and  lower  base,  and  all  edges;  the  drawing, 
however,  shows  a  second  method  of  projecting  the  upper  base, 
by  projecting  the  pyramid  as  a  whole  and  locating  the  upper 
base  by  projecting  the  F  intersections  of  the  edges  with  this 
base  to  the  horizontal  projection  of  the  edges — the  same  method 
as  given  for  the  first  projection  of  this  base. 

Development. — To  develop  means  to  unfold,  and  assuming 
the  frustum  to  be  hollow — made  of  sheets  of  pasteboard  or  metal — 
let  it  be  required  to  develop  it.  It  is  evident  that  in  the  develop- 
ment each  base  and  every  side  will  show  in  its  true  size  and  length. 
The  true  size  of  the  two  bases  is  known  (the  lower  base  being 


PROJECTION.  6 1 

in  the  horizontal  plane,  and  projected  in  i  in  its  true  size),  now 
to  obtain  the  true  length  of  each  of  the  six  sides. 

Since  the  pyramid  is  a  right  pyramid,  all  of  its  edges  are  of 
equal  length;  the  drawing,  however,  shows  the  edges  of  unequal 
lengths:  four  of  them,  being  oblique  to  both  V  and  H,  show  a 
length  less  than  the  true  length,  and  two,  being  parallel  to  F, 
show  on  that  plane  in  their  true  length.  The  true  width  at  the 
bottom  of  each  face  of  the  pyramid  is  known,  this  line  being  in 
the  horizontal  plane  (i).  To  draw  the  development  proceed 
as  follows: 

With  o  (C)  as  a  center,  and  a  radius  equal  to  the  slant  height 
of  the  pyramid — the  true  length  of  an  edge — describe  the  indefinite 
arc  1-2-3,  etc->  now  use  tne  line  o-4  as  a  center  line,  and  from 
its  intersection  with  the  arc,  with  the  true  length  of  the  base  of  a 
side  of  the  pyramid  as  a  unit,  lay  of!  (both  above  and  below  the 
center  line)  on  the  arc  the  lengths  4-3,  3-2,  etc.,  and  join  these 
points  with  each  other,  and  with  the  center,  o;  the  resulting 
drawing  will  represent  the  development  of  the  sides  of  the  pyra- 
mid. To  obtain  the  development  of  the  sides  of  the  frustum, 
find  the  true  lengths  of  the  various  edges  and  transfer  these 
lengths  to  drawing  C. 

Let  the  frustum  be  cut — for  development — along  the  edge  1-7; 
this  edge  being  parallel  to  V  (i)  shows  its  true  length  on  F;  also, 
the  edge  4-0  is  there  projected  in  its  true  length  for  the  same 
reason;  these  lengths,  then,  may  be  taken  directly  from  2.  To 
obtain  the  true  length  of  the  other  four  edges,  each  in  turn  must 
be  revolved  about  o  as  a  center  (i),  until  parallel  to  F,  when 
their  true  lengths  will  be  there  projected,  showing  in  the  drawing 
(2)  as  the  lengths  4-9,  4-8,  etc.,  on  the  slant  height  4-0.  These 
lengths  are  then  laid  off  on  the  proper  line  of  C,  and  the  points  7, 
8,  etc.,  thus  obtained,  when  joined  by  straight  lines,  give  the 
development  of  the  line  of  intersection  of  the  sides  and  upper 
base,  completing  the  development  of  the  sides  of  the  frustum. 

In  the  development,  the  upper  base  should  be  attached  to 
some  point  of  the  line  of  intersection  of  the  sides  with  this  base, 
and  the  lower  base  should  be  attached  to  the  line  of  intersection 


62  MECHANICAL  DRAWING. 

of  the  sides  with  the  lower  base.  These  two  figures,  10  and  9, 
are  copied  from  4  and  3  respectively,  and  placed  as  shown  (C) 
for  balance.  With  C  completed,  if  cut  out  along  the  full-line 
outline  and  folded  together,  it  would  give  the  object  illustrated 
in  Fig.  21. 

79.  PROBLEM  5 . — Projections  of  a  Frustum  of  a  Right  Cone  of 
Revolution,  and  its  Development. — Figs.  23  and  24.  Let  it  be 
required  to  draw  the  projections  of  a  frustum  of  a  right  cone  of 
revolution,  and  to  develop  the  frustum,  the  cone  to  be  assumed 
and  projected  the  same  as  the  pyramid  given  in  Problem  4. 


Fig.  23 


The  Orthographic  Projection  of  the  frustum  of  a  cone^ 

This  problem  is  solved  by  dividing  the  circle  of  the  base  of 
the  cone  into  an  equal  number  of  equal  arcs,  and  joining  these 
points  of  division  with  the  apex  of  the  cone,  thus  giving  a  number 
of  elements  of  the  cone — working  lines — which  are  projected 
through  the  several  drawings  in  the  manner  described  for  the 
six  edges  of  the  pyramid,  with  the  exception  that,  instead  of 
joining  the  projected  points  with  straight  lines,  curved  lines  are 
used.  There  are,  however,  two  elements  which  cannot  be  thus 
projected,  i.e.,  the  center  elements,  C  (V)  and  4-C,  lo-C  (H)\ 
in  locating  the  points  through  which  the  H  projection  of  the 
curve  of  the  upper  base  of  the  frustum  is  to  be  drawn,  it  is  necessary 
to  find  the  points  X  and  Y — the  projection  of  the  intersection 


PROJECTION.  63 

of  the  elements  \-C  and  lo-C  with  the  plane  of  the  upper  base. 
To  locate  these  points,  since  any  section  parallel  to  the  plane 
of  the  lower  base  is  a  circle,  if  a  plane  X-  Y  be  passed  perpendicular 
to  V  and  parallel  to  H,  through  point  C,  it  is  obvious  that  the 


PROJECTION   No.  5. 


NAME. 


DATE. 


Fig.  24. 


distance  from  the  center  of  the  cone  to  point  C  on  the  surface 
is  equal  to  the  radius  C-X  or  C-Y  of  the  circle  cut  by  the  plane 
X-F;  hence  take  the  distance  C-X  or  C-Y  and  lay  it  off  on  the 
line  4-C-io,  as  C-X  and  C-Y,  which  gives  the  required  points. 

80.  PROBLEM  6.  To  Draw  the  Projections  of  the  Intersection 
of  Two  Right  Cylinders  of  Revolution,  and  to  Develop  the  Cylin- 
ders.— Plate  No.  8.  Let  the  cylinders  be  assumed  as  shown  by 
drawings  i  and  2,  Fig.  5,  and  the  first  position  of  Fig.  i. 

To  solve  the  problem,  select  a  number  of  elements  in  each 
cylinder  to  use  as  working  lines;  with  this  in  mind,  pass  a  num- 
ber of  planes,  t-T-f,  which  are  perpendicular  to  both  V  and  H, 
cutting  the  smaller  cylinder,  5,  in  a  number  of  elements,  and  since 
the  two  cylinders  intersect  at  right  angles,  these  same  cutting- 
planes  also  cut  elements  of  the  large  cylinder,  L.  These  planes 
are  passed  through  S,  because  all  such  planes  intersect  both 
cylinders. 

In  drawing  (Fig.  5),  the  method  of  procedure  is  to  divide  the 


64  MECHANICAL  DRAWING. 

small  circle  (i)  into  an  even  number  of  equal  arcs,  and  through 
these  points  of  division  to  draw  the  vertical  lines  as  shown. 

The  first  position  of  the  cylinders  is  one  in  which  the  ele- 
ments of  51  are  parallel  to  H  and  perpendicular  to  F,  and  the 
elements  of  L  are  parallel  to  F  and  perpendicular  to  H.  Through- 
out the  problem,  L  is  assumed  as  resting  on  H. 

The  view  marked  4  presents  a  side  view  of  i,  and  is  obtained 
by  first  constructing  drawing  3,  which  is  a  copy  of  drawing  2, 
turned  90°,  and  then  projecting  vertically  from  3  and  horizontally 
from  i,  and  locating  the  intersection  of  the  projections  of  the 
elements  cut  by  the  same  plane. 

The  view  marked  6  is  an  angular,  side  view  of  i,  and  is  obtain- 
ed by  first  constructing  5,  which  is  a  copy  of  drawing  3,  turned  30° 
to  the  ground  line,  then  projecting  vertically  from  5  and  hori- 
zontally from  4.  The  location  of  the  points  P  and  P  (6)  require 
special  mention. 

When  looking  against  the  vertical  plane,  as  view  6  is  taken, 
one  cannot  see  that  portion  of  the  large  cylinder  beyond  a  section 
parallel  to  F  through  its  center,  in  the  drawing,  beyond  the 
extremes  of  the  horizontal  diameter  through  the  point  N  (5). 
An  inspection  of  the  drawing  shows  no  element- cutting  plane 
through  this  point;  to  project  this  point,  then,  let  an  auxiliary 
element- cutting  plane  be  passed  through  the  point,  and  the  pro- 
jection made  in  accordance  with  the  drawing. 

Assuming  the  cylinders  to  be  hollow  and  with  open  ends,  let 
it  be  required  to  develop  them,  to  roll  them  out  flat,  as  shown  by 

Fig.  3- 

The  Development  of  the  Small  Cylinder. — Lay  off  the  per- 
pendicular line  i- 1  (3,  Fig.  4)  equal  to  the  true  length  of  the 
small  cylinder,  and  draw  the  indefinite  horizontal  lines  i-i. 
Now  take  the  cord  of  arc  1-2  (i,  Fig.  5),  which  is  contained 
twelve  times  in  the  circumference  of  5,  and  lay  it  off  twelve  times 
on  either  of  the  horizontals  i-i,  or  the  center  line  C-C,  and  through 
the  twelve  points  thus  obtained  draw  the  twelve  perpendiculars 
i-i,  2-2,  3-3,  etc.,  completing  the  development  of  the  small  cylin- 
der. It  is  obvious  that  the  greater  the  number  of  arcs  in  5 


PROJECTION. 


65 


PLATE  No.  8. 


AiM,  O 


66  MECHANICAL  DRAWING. 

(i,  Fig.  5),  the  smaller  the  cord  of  the  arc,  and  the  more  nearly 
accurate  the  development. 

In  addition  to  developing  S,  let  it  be  required  to  show  the 
line  of  its  intersection  with  L.  There  are  already  lines  on  the  devel- 
opment representing  the  elements  of  5;  also,  drawing  4  shows 
these  elements  when  parallel  to  V,  and  hence  in  their  true  length. 
The  short  method  of  showing  the  lines  of  intersection  referred  to 
is  as  follows :  Working  from  the  center,  line  C-C  of  drawing  4 
(Fig.  5),  take  the  lengths  showing  the  horizontal  distance  of  the 
various  points  of  the  intersection  i,  2,  3,  etc.,  from  this  center 
line  and  transfer  them  to  the  development  as  the  lengths  C-i, 
C-2,  C-3,  etc.,  and  draw  the  horizontal  lines  as  shown,  giving 
the  points  through  which  the  curve  representing  the  line  of  inter- 
section is  drawn. 

To  Develop  the  Large  Cylinder. — Lay  off  the  vertical  length 
X'  (L,  Fig.  4),  draw  two  horizontal  lines  of  indefinite  lengths 
through  its  extremities,  and  draw  the  center  line  X-Y-X.  Now, 
let  the  cylinder  be  cut  along  the  element  X  (3,  Fig.  5),  and  taking 
the  lengths  of  the  chords  of  the  arcs,  X-4,  4-3,  3-2,  etc.,  until  again 
coming  to  the  point  X,  transfer  them  to  the  development  as 
shown  and  erect  the  dotted  perpendiculars,  which  represent 
those  elements  of  L  cut  by  the  cutting  planes  and  concerned  in 
the  intersection.  In  drawing  3,  the  elements  of  this  cylinder 
are  perpendicular  to  H  and  parallel  to  F,  and  hence  are  pro-: 
jected  on  V  in  their  true  length.  The  short  method  of  showing 
the  development  of  the  intersection  is  as  follows:  Working  with 
the  line  4-4  (4,  Fig.  5)  as  a  center  line,  take  the  lengths  repre- 
senting the  perpendicular  distances  of  the  various  points  of  the 
intersection  i,  2,  3,  etc.,  from  this  center  line  and  transfer  them 
to  the  development  as  the  lengths  4-1,  4-2,  etc.,  and  draw  the 
horizontal  lines  as  shown,  giving  the  points  of  intersection  through 
which  the  two  ellipses,  representing  the  holes  to  receive  the  small 
cylinder,  are  drawn. 

With  the  two  developments  complete,  if  cut  out  along  the 
full  lines  and  rolled  into  cylinders,  it  will  be  found  that  the  two 
can  be  fitted  together  the  same  as  is  illustrated  by  Fig.  i. 


PROJECTION.  67 

81.  PROBLEM  7.  To  Draw  the  Projections  of  the  Intersection 
of  a  Right  Cone  of  Revolution  with  a  Right  Cylinder  of  Revolu- 
tion, and  to  Develop  Both. — Plate  No.  9.  Let  the  objects  be 
assumed  as  by  drawings  i  and  2,  Fig.  5,  and  drawing  i,  Fig.  i. 
To  solve  the  problem  select  a  number  of  intersecting  elements 
in  each  figure  and  project  these  elements  as  in  thj  previous 
problem. 

To  select  the  elements  to  be  projected,  pass  a  number  of  planes, 
t-i-T,  t-2-T,  etc.  (Fig.  5),  perpendicular  to  V  and  at  various 
angles  with  H,  through  the  apex  of  the  cone  and  intersecting  the 
cone  and  cylinder  along  elements,  the  practical  method  being  to 
divide  the  circle  of  the  base  of  the  cone  into  an  equal  number  of 
equal  arcs,  to  project  these  divisions  to  the  vertical  projection 
of  the  base  and  then  to  join  these  points  of  division  with  the 
apex.  These  lines,  then,  represent  the  projections  of  the  elements 
of  the  cone  which  are  to  be  deak  with;  the  elements  cut  from  the 
cylinder  by  the  same  intersecting  planes  are  clearly  shown  by  the 
drawing. 

To  horizontally  project  the  intersection  of  the  two  figures  (the 
two  ellipses  shown  in  2),  project,  vertically,  from  the  points  of 
intersection  of  the  circle  of  the  base  of  the  cylinder  with  the 
different  elements  of  the  cone  (i)  to  the  horizontal  projection 
of  the  elements  of  the  cone — the  radial  lines  of  2 — as  in  Problem  5. 
It  is  obvious  that  the  small  ellipse  represents  the  visible  portion 
of  the  horizontal  projection  of  the  intersection  and  the  large 
ellipse  the  hidden  portion;  the  case  in  hand  is  one  of  penetra- 
tion— the  cone  penetrating  the  cylinder. 

Drawing  3,  Fig.  5,  is  a  copy  of  drawing  2,  turned  90°,  and 
drawing  4  is  obtained  by  projecting  horizontally  from  i  and 
vertically  from  3,  the  lines  of  intersection  being  obtained  by 
projecting  horizontally  from  the  intersection  of  the  circle  of  the 
base  of  the  cylinder  with  the  different  elements  of  the  cone  (i) 
to  the  various  elements  of  the  cone  as  shown  in  4.  The  horizontal 
projection  of  the  intersections  (3)  are  obtained  by  projecting 
vertically  from  the  points  of  intersection  shown  in  4  to  the  hori- 
zontal projections  of  the  elements  of  -the  conc-^the  radial  lines. 


63 


MECHANICAL  DRAWING. 


PLATE  No.  9. 


PROJECTION.  69 

To  Develop  the  Cylinder. — Drawings  i  and  4,  Fig.  5,  show  an 
end  and  side  view  of  the  cylinder,  respectively,  the  elements  showing 
in  their  true  lengths  in  the  side  view;  to  develop  the  cylinder, 
draw  the  vertical  line  L-L,  Fig.  2,  and  draw  the  two  indefinite 
horizontal  lines  L-L.  Now,  working  from  the  circle  of  drawing  i, 
Fig.  5,  and  assuming  the  cylinder  to  be  cut  along  element  L,  take 
the  length  of  the  chord  of  the  arc  L-K  and  lay  this  length  off  on 
the  development  as  the  horizontal  length  L-K]  next  take  the 
chord  of  the  arc  K-J  and  transfer  it  to  the  development  in  the 
manner  shown,  and  so  on,  taking  each  chord  in  turn  until  again 
at  the  point  L,  when  the  length  of  the  horizontal  line  L-L  will  be 
determined  and  is  approximately  equal  to  the  distance  around 
the  cylinder — the  circumference.  It  should  be  noted  that  the 
arcs  H-X  and  P-Q  are  bisected,  rendering  the  length  of  the 
development  more  nearly  equal  to  the  length  of  the  circumference 
of  the  cylinder  than  if  the  chords  of  the  above  arcs  had  been  used. 

Each  point  of  division  along  the  horizontals  L-L  represents 
the  locus  of  an  element  of  the  cylinder,  which,  when  connected 
by  the  perpendiculars  L-L,  K-K,  etc.,  locate  the  elements  required 
to  find  the  development  of  the  lines  of  intersection,  the  points  of 
intersection  being  found  as  follows:  Take  the  true  lengths  of 
L-f,  M-gj  etc.,  from  drawing  4,  transfer  them  to  the  development 
as  shown,  and  connect  the  points  thus  obtained  with  a  curved 
line. 

To  Develop  the  Cone.— With  o  (Fig.  4)  as  a  center  and  a 
radius  o-i  (i,  Fig.  5)  equal  to  the  slant  height  of  the  cone 
(the  true  length  of  the  elements),  describe  the  indefinite  arc  i-i. 
Now  the  base  of  the  cone  has  been  divided  into  twelve  equal 
arcs,  and  since  the  length  of  the  arc  i-i  must  equal  the  length  of 
the  circumference  of  the  base  of  the  cone,  take  the  chord  of  one 
of  these  arcs  and  step  it  off  twelve  times  along  the  arc  i-i, 
then  join  these  points  of  division  with  the  center,  o;  this  gives 
a  drawing  representing  the  development  of  the  cone. 

To  show  the  line  of  intersection  of  the  cone  with  the  cylinder, 
the  true  length  of  each  element  from  the  base  or  from  the  apex 
of  the  cone  to  its  point  of  intersection  with  the  cylinder  must  be 


DRAWING. 

taken  from  either  drawing  i  or  4  by  horizontally  projecting 
each  point  of  intersection  onto  the  slant  height — a  short  method 
of  revolving  parallel  to  V — as  in  Problem  5,  and  transferred  to 
the  development  as  shown. 

82.  PROBLEM  8.  To  Find  the  Intersection  of  Two  Right  Cyl- 
inders of  Revolution  which  Intersect  at  an  Angle. — Fig.  25.  This 
problem  is  met  with  in  the  drawing  of  pipe  fittings,  boilers,  etc., 
wherever  it  is  required  to  represent  the  intersection  of  two  cylin- 
ders. 

12.34  ,  4321 

T 


Analysis. — Intersect  the  two  cylinders  with  a  system  of  planes, 
T1,  r,  T1,  etc.,  which  cut  elements  from  both  cylinders  (as  indi- 
cated by  the  ruled  section)  and  find  the  intersection  of  the  ele- 


PROJECTION. 


ments  of  each  cylinder  cut  by  the  same  plane;  these  points, 
when  joined  by  a  curved  line,  represent  the  line  of  intersection 
of  the  cylinders. 

Solution. — Draw  the  semicircles  M  and  N  and  divide  them 
into  an  equal  number  of  equal  arcs;  through  these  points  of  divi- 
sion draw  the  lines  i-i,  2-2,  etc.,  parallel  to  the  elements  of  cylin- 
der A .  From  the  points  of  intersection  of  these  lines — elements — 
with  the  circle  of  the  large  cylinder,  B  (the  plan  drawing),  project 
to  the  elevation  to  an  intersection  with  the  elevation  of  the  same 
elements  and  join  the  points  thus  obtained,  as  shown. 

The  developments  are  made  as  in  Problem  6. 


The  Development 
of  cylinder 


10 


11 


12 


83.  PROBLEM  9.  To  Construct  a  Conical  Paper  Shade  for  an 
Ordinary  Incandescent  Lamp. — Let  the  drawing  for  the  pro- 
posed shade  be  that  given  in  plan  and  elevation,  Fig.  27. 

Analysis. — If  the  sides  D-A  and  C-B  of  the  shade  be  projected 
to  an  intersection  at  O,  the  shade  becomes  a  cone,  which,  when 
developed  and  a  proper  allowance  made  for  lap,  may  be  cut  from 
the  paper  and  rolled  into  the  required  shade. 

Solution. — Produce  the  lines  D-A  and  C-B  as  suggested,  and 
with  the  length  O-A  as  a  radius,  and  with  O,  Fig.  28,  as  a  center, 
describe  the  indefinite  arc  B-B'.  Now  divide  the  circumference 
of  the  plan  of  the  base  of  the  cone  into  an  equal  number  of  equal 
arcs;  take  the  chord  of  one  of  these  arcs  and  step  it  off  along  B-B' 
the  same  number  of  times  it  is  contained  in  the  circumference 
of  the  plan  of  the  base;  from  the  two  extremes  of  the  thus  deter- 


MECHANICAL   DRAWING. 


FIG.  27. 


c' 


The  Shade  (Developed 


IA 

FIG.   28. 


PROJECTION. 


73 


mined  arc  draw  lines  to  the  center  O.  Now  take  a  radius  equal 
to  O-D  of  the  elevation  drawing  and  describe  the  arc  C-C,  ter- 
minating in  the  radial  lines  from  the  center  to  the  extremes  of 
arc  B-B'.  To  allow  for  lap,  produce  the  arcs  C-C  and  B-G  as 
shown,  and  terminate  them  with  a  line  parallel  to  C-B  at  the 
required  distance;  cut  out  along  the  heavy  line  outline  (other 
lines  being  construction  lines),  fold  up,  and  paste  or  pin  the  lap; 
that  is,  securely  fasten  the  ends  with  C-B  and  C-B  coincident, 
and  the  shade  is  finished. 

84.  First  and  Third  Quadrant  Projections. — In  mechanical 
drawing,  it  is  often  convenient  to  draw  the  plan  of  an  object 
below  the  elevation — a  procedure  which  is  in  strict  accordance 
with  the  principles  of  projection,  and  a  correct  one  in  every  way. 


FIG.  30. 


Referring  to  Figs.  29  to  32,  inclusive,  Fig.  29  illustrates  the  first 
quadrant  projection  of  an  object,  Fig.  30  representing  the  con- 
ventional projection.  It  will  be  noted  that  in  this  drawing  the 
plan  is  below  the  elevation.  Now  assume  the  object  to  be  trans- 
ferred to  the  third  quadrant  as  in  Fig.  32  and  here  (Fig.  31)  the 
plan  is  above  the  elevation;  hence  when  the  plan  of  an  object 
is  drawn  above  the  elevation  the  object  is  assumed  to  be  situ- 
ated in  the  third  quadrant  and  the  drawing  said  to  be  a  third- 
angle  drawing  or  projection;  when  the  plan  is  drawn  below 


74 


MECHANICAL   DRAWING. 


the  elevation,  the  drawing    is  a  first-angle  drawing  or   projec- 
tion. 


— 1 1 L 

U L_T 


FIG.  31. 


85.  Isometric  Projection. — In  the  orthographic  projections 
treated  of  thus  far  the  objects  projected  have  been  so  situated 
relative  to  the  planes  of  projection  as  to  project  but  one  face  of 
the  object  on  each  plane,  and  this  is  the  usual  practice.  It  is, 
however,  often  desirable  to  project  two  or  more  faces  of  an  ob- 
ject onto  one  plane  of  projection,  that  a  general  conception  of 
the  object  may  be  obtained  from  the  one  projection  or  draw- 
ing. To  construct  a  scenographic  projection,  which  is  obtained 
mechanically  from  and  after  the  usual  orthographic  projections 
have  been  constructed,  requires  much  time  and  labor,  and  because 
of  the  complicated  arrangements  occurring  in  machinery  is  prac- 
tically useless  for  such  work.  There  is,  however,  a  method  of 
assuming  objects  to  be  so  situated  with  respect  to  the  planes  V 
and  H  as  to  orthographically  project  two  or  more  of  its  faces 
on  each  plane;  such  an  arrangement  may  be  called  an  "oblique" 
orthographic  projection. 

There  is  a  special  case  of  oblique  orthographic  projection, 
called  "isometric"  projection,  which  portrays  three  faces  of  an 
object,  is  comparatively  easy  of  construction,  and  is  well  adapted 
to  the  representation  of  fairly  simple  objects;  particularly  is  it 


PROJECTION. 


75 


convenient  and  specially  adapted  to  the  representation  of  rect- 
angular objects  or  objects  in  which  the  principal  lines  are  straight, 
parallel  lines,  as  in  the  frame  of  a  building.  Having  three  faces  to 
depict,  there  are  three  dimensions  to  be  considered:  (i)  length,  (2) 
breadth — both  horizontal  dimensions— and  (3;  height— a  vertical 
dimension.  , 

Let  it  be  required  to  construct  an  orthographic  projection  of 
a  cube,  the  projection  to  show  equal  amounts  of  three  adjacent 
faces.  It  is  evident  that  to  portray  equal  amounts  of  three 
adjacent  faces  of  the  cube,  it  must  be  assumed  to  occupy  a  position 
relative  to  the  plane  of  projection,  such  that  one  of  its  diagonals 
will  be  perpendicular  to  the  plane.  Fig.  33  is  a  representation 


FIG.  33 


of  the  proposed  arrangement.  Having  three  faces  projected, 
the  projection  on  but  one  plane  is  all  that  is  necessary  to  "  tell  the 
story."  The  vertical  plane  is  the  one  adopted.  Fig.  34  is  a 
mechanical  drawing  of  the  arrangement,  A  being  a  side  view 
of  the  cube  and  V-V  a  side  view  of  plane  V.  It  will  be  ob- 
served that  the  line  6-O — a  diagonal  of  the  cube — is  perpendicular 
to  the  plane  of  projection.  The  drawing  marked  B  is  a  front 
view  of  the  plane  V-V,  showing  the  orthographi?  Projection  of 


76 


MECHANICAL   DRAWING. 


the  cube  when  thus  assumed,  and  is  now  called  the  "isometric" 
projection  of  the  cube. 

It  will  have  been  noted  in  orthographic  projection  that  a 
line  is  projected  in  its  true  length  only  when  parallel  to  the  plane 
of  projection.  It  is  evident  in  the  above  case  that  the  lines — 


FIG.  34 


edges — O-i,  0-3,  and  0-4  make  equal  angles  with  the  plane  F-F, 
and  making  equal  angles,  will  be  projected  on  that  plane  in  equal 
lengths,  which  lengths,  however,  are  somewhat  less  than  the 
true  lengths,  being  foreshortened  (equally)  in  projection.  The 
angle  noted  is  an  angle  of  35°- 16',  and  the  projected  length  is 
proportional  to  this  inclination,  being  approximately  equal  to 
.8  of  the  true  length. 

Referring  to  Fig.  34  again,  and  remembering  that  the  three 
adjacent  edges  O-i,  0-3,  and  0-4  of  the  cube  form  right  angles, 
it  will  be  noted  that  the  projected  angles  between  these  lines  are 
equal — equal  to  120°.  These  three  lines  form  the  basis  of  opera- 
tion in  isometric  projection  and  drawing  and  are  called  the 
"coordinate  axes."  The  perpendicular  diagonal  of  the  cube 
is  called  the  isometric  axis  and  the  common  point  of  intersec- 
tion, O,  is  called  the  origin.  Fig.  35  is  a  representation  of  the 
coordinate  axes,  showing  an  optional  notation  for  the  three 
dimensions  of  isometric  projection  and  drawing. 

There  is  a  distinction  between  isometric  "projection"  and 
isometric  "drawing,"  which  can  be  illustrated  by  the  case  of 


PROJECTION. 


77 


the  cube.  Fig.  34,  B,  is  an  isometric  "projection"  of  the  cube, 
and,  as  has  been  explained,  the  length  of  the  sides  of  the  projec- 
tion are  but  .8  of  the  true  length  of  an  edge  of  the  cube;  in  an 
;sometric  "drawing"  it  is  customary  to  draw  the  lines  represent- 


20 — . 


Co-ordin  ate  Axes. 


FIG.  35. 

ing  the  edges  of  the  cube  of  a  length  equal  to  the  true  length  of 
an  edge;  as,  for  example,  suppose  one  has  a  i-inch  cube  to 
project  and  to  draw,  the  lines  of  the  projection  will  be  .8  inch 
long,  while  the  lines  of  the  drawing  will  be  i  inch  long. 

To  illustrate  the  application  of  the  principles  of  isometric 
projection  to  practical  draughting — the  construction  of  isometric 
drawings — let  it  be  required  to  construct  an  isometric  drawing 
of  an  object  the  mechanical  drawing  of  which  is  shown  in  A, 
Fig.  36.  Having  three  faces  to  show,  there  are  three  dimensions: 
1  =  length,  b  =  breadth,  and  h  =  height.  Now  assume  the  object 
to  be  inclosed  by  a  rectangular  box,  as  is  indicated  by  the  dotted 
lines,  the  three  dimensions  of  the  box  corresponding  with  the 
three  extreme  dimensions  of  the  object — /,  6,  and  h. 

Having  such  an  assumption  in  mind,  the  isometric  drawing 


?8  MECHANICAL   DRAWING. 

of  the  object  may  be  begun,  the  first  step  of  which  (Fig.  36)  is  to 
draw  the  coordinate  axes  and  assume  one  line  to  represent  length,  /, 
one  to  represent  breadth,  b,  and  one  to  represent  height,  h.  The 
second  step  is  to  lay  off  on  the  co-ordinate  axes  /,  6,  and  h  lengths 
corresponding  to  /,  b,  and  h  of  the  mechanical  drawing,  af.er 
which  complete  the  isometric  drawing  of  the  inclosing  box  by 
drawing  lines  from  the  extremities  of  these  three  lengths  parallel 
to  the  co-ordinate  axes,  as  shown.  The  third  step  of  the  draw- 
ing is  to  draw  those  lines  visible  in  some  one  face  of  the  box.  In 
Fig.  36  this  "one  face"  is  the  top  face;  in  like  manner  the' fourth 
and  fifth  steps  are  executed  by  drawing  those  lines  visible  in  the 
front  and  right  faces,  respectively.  The  sixth  step  is  to  draw 
all  other  visible  lines,  and  the  seventh  step  to  erase  all  construc- 
tion lines,  giving  a  finished  isometric  drawing. 

To  Dimension  an  Isometric  Drawing. — Mechanical  drawings 
are  dimensioned  in  two  directions,  (i)  horizontal  and  (2)  vertical; 
in  isometric  drawing  the  dimensions  are  drawn  parallel  to  the 
coordinate  axes.  An  isometric  drawing  is  rarely  used  for  shop 
purposes,  that  is,  as  a  working  drawing  having  all  dimensions 
given,  etc.,  except  for  representing  very  simple  rectangular  objects, 
being  most  useful  as  a  drawing  for  illustration  and  not  for  direc- 
tion or  instruction. 

An  isometric  drawing  intended  for  shop  purposes  should  be 
completely  and  properly  dimensioned  and  noted,  eliminating  all 
possible  necessity  for  the  workman  to  "scale"  the  drawing;  how- 
ever, should  it  be  required  to  scale  an  isometric  drawing,  the 
scaling  must  be  done  in  the  direction  of  the  coordinate  axes. 

Isometric  Scales. — As  has  been  described,  the  usual  and 
practical  method  of  constructing  isometric  drawings  is  to  draw 
the  lines  of  the  drawing  of  the  same,  or  some  standard  proportional 
length  of  the  line  of  the  object  each  represents,  remembering  that 
the  "  isometric  dimensions"  are  measured  in  directions  parallel  with 
the  direction  of  the  coordinate  axes;  however,  for  some  special 
reason  one  may  have  occasion  to  construct  an  isometric  projection 
of  an  object.  To  construct  such  a  drawing  it  is  first  necessary 
to  construct  an  isometric  scale — a  scale  on  which  all  the  dimen- 


PROJECTION. 


79 


8o 


MECHANICAL  DRAWING, 


sions  are  properly  foreshortened,  as  i  inch  will  be  represented 
by  a  length  .8  inch  long.  The  scale  is  constructed  by  laying 
off  the  scale  B,  Fig.  37,  the  left  side  of  which  is  graduated  into 
full:length  inches  and  subdivisions,  then  projecting  horizontally 
to  scale  A,  the  right  side  of  which  is  the  foreshortened  isometric 
scale. 


Isometric  Scales. 


ft  — 

CO 

- 

CO 

"A" 

C\J 

^J1 

_      < 

fc 

FIG.  37 


To  use  scale  A  for  the  construction  of  isometric  projections, 
the  object  is  measured  with  the  left  side  of  the  scale — the  full- 
length  scale — and  the  projection  constructed  with  the  right  side 
of  the  scale. 

By  referring  to  Fig.  37  again  it  is  seen  that  the  full-length 
inches  of  A  (those  on  the  left)  when  projected  horizontally  to  the 
right  side  of  B  are  1.2  inches  long;  hence  an  isometric  "drawing" 
is  1.2  times  the  size  of  the  object. 

These  isometric  scales  have  no  practical  use  and  are  given 
only  as  a  matter  of  information  in  case  one  should  ever  wish  to 
employ  such  a  scale. 

86.  Elementary  Examples.  —  Let  it  be  required  to  construct 
an  isometric  drawing  of  a  cube  each  of  whose  faces  contains  a 


PROJECTION. 


81 


circle  of  the  same  diameter  as  the  dimension  of  the  cube.  Let 
the  drawing  of  the  cube  be  constructed  in  accordance  with  the 
instructions  already  given  (Fig.  38).  Now  to  draw  the  circle 
within  the  top  face,  A-B-C-O,  since  it  will  be  tangent  at  the  middle 
point  of  each  side  of  the  rhombus  A-B-C-O,  locate  this  point  of 


each  side,  and  with  a  center  at  B  and  a  radius,  R,  equal  to  the 
distance  from  B  to  Y  (the  middle  point  of  the  opposite  side  of  the 
rhombus)  draw  the  arc  Y-Y  (the  long  one),  then  with  the  point 
O  as  a  center,  and  with  the  same  or  equal  radius,  O-F,  describe 


FiQ.  39. 


FIG.  40.   ' 


the  second  long  arc  Y-Y]  next  draw  the  diagonal  C-A,  and 
with  the  points  Xy  X — the  points  in  which  this  diagonal  cuts 
the  lines  B-Y  and  O-Y — as  centers,  and  a  radius,  5,  equal  to  the 
distance  from  X  to  the  points  F,  F,  complete  the  ellipse  Y-Y -Y-Y 
— the  isometric  drawing  of  the  circle  in  the  top  face  of  the  cube. 


82  MECHANICAL  DRAWING. 

The  ellipses  of  the  right  and  left  faces  are  drawn  in  like  manner. 
This  is  the  method  of  constructing  all  circles  and  circular  arcs 
in  isometric  drawing,  i.e.,  to  first  inclose  the  circle  within  a  square, 
then  to  draw  the  square  in  isometric,  then  the  circle  as  directed. 

Examples  of  simple  isometric  drawings  are  given  in  Figs.  39 
and  40,  and  in  the  various  Plates. 


CHAPTER  IV. 

DRAWING  TOOLS  AND  MATERIALS. 

87.  Introductory. — As  all  drawings  consist  of  either  straight 
or  curved  lines,  entire  or  in  combinations,  and  since  in  mechanical 
drawing  these  lines  must  be  exact,  the  student  in  draughting 
must  provide  himself  with  a  number  of  mechanical  devices, 
technically  termed  "instruments,"  calculated  to  facilitate  his  labor 
and  precision. 

In  draughting,  as  in  all  manual  labor,  the  skill,  natural  or 
acquired,  of  the  "operator"  is  a  potent  factor  in  securing  results; 
however,  in  the  selection  of  instruments  this  factor  should  be 
disregarded  and  the  best  instrument  selected  that  can  be  afforded; 
for  granted  a  skilled  draughtsman  may  execute  a  fair  drawing 
with  inferior  instruments,  how  much  better  work  might  he  do 
with  the  very  best;  for  the  unskilled  it  is  obvious  the  "very  best" 
is  none  too  good.  The  beginner  should  not  think  "anything  will 
do  to  begin  with,"  promising  himself  to  provide  an  Ai  outfit 
when  he  shall  have  acquired  a  fair  degree  of  proficiency.  Accuracy 
is  one  of  the  first  requisites  of  a  mechanical  drawing  and  cannot 
be  secured  with  poor  tools. 

Having  recognized  the  necessity  of  proper  equipment,  the  ques- 
tion "What  'make'  of  instrument  is  the  best"  confronts  the 
prospective  purchaser.  Of  all  of  the  numerous  "makes"  on 
the  market,  there  may  be  said  to  be  two  general  classes:  (i)  the 
instrument  of  triangular  section  and  (2)  the  instrument  of  circular 
section.  (See  Figs.  48  and  49.)  Consultation  with  experienced 
draughtsmen  will  elicit  the  information  that  there  is  a  charac- 
teristic of  instruments  called  the  "feel"  of  the  instrument,  mean- 
ing the  sensation  produced  on  the  nerves  by  the  handling  of  the 
tool,  one  draughtsman  preferring  the  first  class  of  instrument 

83  > 


84 


MECHANICAL   DRAWING. 


because  of  its  "feel,"  its  "touch"  when  in  his  hand,  and  another 
draughtsman  preferring  the  second  class  of  instrument  for  the 
same  reason,  it  being  simply  a  case  of  what  the  man  is  accus- 
tomed to. 

The  selection  of  instruments,  then,  becomes  a  question  as 
to  details  of  construction,  and  is  a  matter  of  finance  and  choice  with 
the  buyer,  he  being  "safe"  in  purchasing  a  good  quality  of  any 
of  the  standard  makes. 


FIG.  41. 

i.  Compass  with  pencil-leg  and  needle-point.  2.  Hair-spring  dividers. 
3.  Lengthening-bar.  4.  Pen-leg.  5,  6.  Ruling -pens.  7.  Lead -box.  8.  Bow 
pencil.  9.  Bow  dividers.  10.  Bow  pen. 

"Just'  what  tools  are  necessary,  what  to  buy,"  is  the  next 
question,  and  is  one  of  much  latitude,  since  there  are  tools  and 
devices  to  be  had  by  the. score.  As  in  every  question,  there  are 


DRAWING    TOOLS  AND  MATERIALS.  85 

two  sides  to  be  considered:  (i)  what  can  one  get  along  with,  and 
(2)  what  ought  one  to  have?;  the  answer  to  the  first  being 
instruments  for  drawing  straight  and  curved  lines,  representing  few 
tools  and  a  minimum  outlay,  while  for  the  second  question  it  might 
be  said  that  many  tools  were  desirable,  representing  a  maximum  out- 
lay. Of  these  two  extremes  a  mean  is  taken,  and  the  following  list 
names  the  articles  that  should  comprise  a  good,  practical  " outfit": 
i.  A  case  of  instruments,  to  consist  of 

2  ruling-pens,  i  large,  i  small. 

i  compass,  with  pen  and  pencil-legs  and  extension-bar. 
i  pair  dividers,  with  hair-spring  adjustment. 

3  bow -instruments:  (i)  pen,  (2)  pencil,  and  (3)  dividers, 
i  box  leads,  hard  and  medium  grades. 

2.  Drawing-board. 

3.  T  square. 

4.  2  Triangles:  (i)  45°  and  (2)  3o°-6o°. 

5.  Irregular  curve. 

.  6.  Architect's  scale. 

7.  Thumb-tacks. 

8.  Pencil,  hard  lead-HHHHHH. 

9.  Pen  and  penholder. 

10.  Erasers — pencil  and  ink. 

11.  Ink,  black. 

12.  Rag  for  cleaning  instruments. 

13.  Blotter. 

14.  Soapstone  pencil. 

The  instruments  named  under  item  i  can  be  secured  sepa- 
rately; the  "trade,"  however,  provides  a  neat  and  convenient  case 
(Fig.  41)  for  the  tools,  and  as  the  additional  cost  of  the  case  is 
small  when  coritpared  with  the  cost  of  new  instruments,  it  is  ad- 
visable to  purchase  a  case;  the  tools  will  then  have  a  proper  recep- 
tacle, and  with  ordinary  care  this  will  minimize  the  necessity 
of  purchasing  new  tools. 

88.  The  Ruling-pen. — Since  the  major  portion  of  most  draw- 
ings is  composed  of  straight  lines,  the  ruling- pen  easily  becomes 
the  instrument  of  prime  importance.  The  first  requisite  of  a 


86  MECHANICAL   DRAWING. 

good  ruling- pen  is  that  the  temper  shall  be  just  right;  it  must 
not  be  too  soft,  rendering  frequent  sharpening  necessary;  neither 
must  it  be  hardened  to  a  degree  rendering  it  brittle  and  susceptible 
to  fracture.  The  "temper"  is  a  quality  which  cannot  be  recog- 
nized by  the  eye  alone  because  of  the  high  polish  given  the  tool; 
the  instrument  must  be  given  a  trial  and  if  not  of  the  proper  degree 
of  hardness  it  may,  provided  the  stock  be  right,  be  retempered. 
Apropos  of  further  discussion,  let  the  student  acquaint  himself 
with  the  names  of  the  various  parts  of  the  ordinary  instrument 
(Fig.  42). 

The  handle  is  usually  of  bone,  wood,  or  metal,  and 
can  be  homogeneous  with  the  nibs,  or  separate  and 
fastened  thereto,  as  is  usually  the  case,  in  the  which 
the  handle  should  always  have  a  firm  and  secure  fit, 
as  any  slight  looseness  will  tend  to  render  the  work  of 
the  pen  inaccurate. 

The  nibs  are  the  "pen,"  and  in  the  ordinary  instru- 
ment are  fashioned  with  a  tendency  to  spring  apart, 
a  tendency  for  the  pen  to  remain  "open";  that  they 
may  be  brought  together,  the  thumb- screw  is  em- 
ployed, only  one  nib  being  threaded,  the  other  having 
a  smooth-bored  hole. 

The  thumb-screw  should  have  a  knurled  head  (the 
edge  cut  into  small  points)  that  it  may  be  easily  oper- 
ated, and  its  shank  should  be  threaded  to  the  head,  or 
otherwise  so  fashioned  that  when  in  position  it  is 
capable  of  bringing  the  nibs  exactly  together.  The 
thread  of  the  screw  should  never  be  allowed  to  become 
corroded,  but  should  be  frequently  oiled  with  gun  or 
bicycle- oil.  The  fit  of  the  screw  in  the  nibs  should 
be  snug  and  even;  there  should  be  no  "binds"  or 


bflD 


The  "business  end"  of  the  pen,  for  ordinary  work, 
should  be  slightly  rounded  as  A,  Fig.  43,  not  like  B\ 
the  nibs  should  be  exactly  of  the  same  length,  ground 
to  a  knife-edge — not  a  point — and  free  from  "burrs"  inside  and 


DRAWING    TOOLS  AND  MATERIALS.  87 

out.     A  new  pen  is  usually  ready  for  use,  and  the  student  will  do 
well  to  carefully  note  the  shape  and  sharpen  of  it. 


FIG.   43. 

A  pen  "in  condition"  and  properly  handled  should  rule  a 
smooth  and  even  line  (i,  Fig.  44)  of  uniform  width  and  with  clean- 
cut  sides;  also,  the  pen  should  produce  lines  varying  in  thickness 
from  a  light  "hair"  line  to  a  heavy  line  of  one-sixteenth  of  one 
inch,  or  greater,  in  width.  Since  the  best  pens  cannot  for  a  great 
while,  in  use,  maintain  an  edge  sufficiently  fine  to  produce  the 
hair  line,  it  is  well,  having  two  pens,  to  reserve  the  small  pen  for 
light  lines  and  the  larger  pen  for  heavy  lines. 

A  pen  "out  of  condition"  will  rule,  if  at  all,  rough,  ragged, 
and  intermittent  lines.  Some  of  the  common  causes  for  such 
results  are:  one  nib  may  be  longer  than  the  other,  the  pen  may 

1." 


FIG.  44. 

be  too  pointed,  there  may  be  burrs  or  rough  places  on  the  points, 
and  above  all  the  pen  may  not  be  held  properly.  In  testing  a 
pen,  a  ruling  edge  should  always  be  employed. 

When  a  pen  produces  a  line  like  2  or  3,  Fig.  44,  one  of  the 
nibs  will  be  found  to  be  longer  than  the  other;  a  line  like  4  indicates 
that  the  pen-points  are  not  smooth — a  small  nick  may  be  broken 


88  MECHANICAL   DRAWING. 

out.  These  are  usually  the  troublesome  features  encountered 
when  only  heavy-  and  medium  weight  lines  are  desired;  the  hair 
line  is  more  difficult  to  draw  and  requires  the  clever  manipula- 
tion of  a  pen  in  the  best  condition.  To  rule  very  tine  lines  the 
pen  must  be  sharpened  to  a  nicety;  a  line  like  5  is  the  product  of 
a  dull  pen,  and  is  the  result  of  attempting  a  liner  line  than  the 
pen,  as  sharpened,  will  rule.  When  such  results  are  obtained, 
let  the  draughtsman  stand  with  his  back  to  the  light,  and  holding 
the  pen  lengthwise  and  in  line  with  the  eye,  look  directly  onto 
the  points  of  the  pen — the  points  of  the  nibs — and  he  will  observe 
two  " bright  spots";  the  finest  line  that  can  be  ruled  with  the 
pen  is  a  line  whose  width  is  the  sum  of  the  widths  of  the  two 
bright  spots,  and  the  pen  being  closed,  the  ink  must  flow  by  con- 
vection around  the  points  and  not  through  or  between  them  as 
it  should,  and  the  flow  being  irregular,  produces  a  line  as  shown. 

The  lines  depicted  in  4  and  5  may  also  be  caused  by  a  dirty 
pen;  ink  may  have  been  allowed  to  dry  on  the  points;  a  thorough 
cleaning  is  the  remedy.  No.  5  may  also  result  from  undue  pres- 
sure on  the  pen  in  the, ruling.  In  ruling  fine  lines  the  pen  should 
be  well  cleaned  after  every  charge  of  ink  has  become  exhausted. 

When  a  pen  is  "out  of  condition,"  the  remedy  is  to  regrind 
it — sharpen  it.  The  manufacturers  of  instruments  maintain  a  de- 
partment for  the  sharpening  of  pens,  repairs,  etc.,  but  should  one 
send  his  pen  to  the  factory  every  time  it  needed  regrinding,  he 
would  justly  forfeit  his  title  of  "Practical  Draughtsman. "  Every 
draughtsman  should  be  able  to  keep  his  instrument  in  first-class 
condition,  for  while  there  are  some  general  instructions  which 
may  be  given  for  the  proper  handling  of  the  pen,  draughting  is 
like  writing;  no  two  men  will  hold  the  pen  in  exactly  the  same 
position,  and  the  pen  must  be  sharpened  to  suit  the  user. 

To  sharpen  a  pen,  close  the  nibs  until  they  have  contact, 
and  with  a  fine-grained  oil-stone  at  hand,  round  off  the  points 
until  they  are  even  and  in  shape,  comparing  with  A,  Fig.  43, 
not  B.  Now  note  the  bright  spots;  these  must  be  ground  away, 
the  pen  must  be  really  sharpened — the  same  as  a  knife-blade — 
not  pointed.  To  do  this,  open  the  nibs,  and  taking  them  one 


DRAWING    TOOLS  AND  MATERIALS  89 

at  a  time,  consider  it  as  a  chisel  or  knife-blade  to  be  sharpened 
on  but  one  side — the  outside — and  by  moving  it  back  and  forth, 
turning  it  slightly  from  side  to  side,  grind  the  points  until  no 
bright  spots  are  visible.  Great  care  must  be  exercised  in  the 
operation,  else  the  point  at  which  the  " spots"  disappear  be 
passed  and  the  nibs  become  of  uneven  lengths,  necessitating 
another  trial  of  the  entire  operation.  A  careful  procedure  should 
produce  a  pair  of  nibs  of  even  length,  truly  and  smoothly  shaped 
and  sharpened  on  all  sides;  should  any  burrs  occur,  however,  at  a 
point  that  cannot  be  treated  with  an  oil-stone  or  oil-slip,  they 
may  be  removed  by  the  use  of  very  fine  emery -rloth. 

To  try  the  pen,  secure  a  piece  of  drawing  paper  and  a  straight- 
edge, and  having  thoroughly  wiped  all  oil  and  dirt  from  the  nibs, 
screw  them  together  until  about  T1/'  to  3V"  apart,  and  charge  the 
pen  with  ink  in  such  quantity  as  will  fill  it  for  about  one-quarter  of 
an  inch  from  the  point  (Fig.  45).  (To  charge  the  pen,  take  the  tool 
in  the  left  hand,  if  right-handed,  and  taking  the  stopper  from 


FIG.  45.  FIG.  46. 

the  ink-bottle  in  the  right  hand,  insert  the  point  of  the  quill  between 
the  nibs,  when  the  ink  will  run  into  the  pen.)  The  pen  being 
charged,  transfer  it  to  the  right  hand  and  manipulate  the  straight- 
edge with  the  left  hand;  hold  the  pen  with  the  thumb-screw  on 
the  outside — away  from  the  hand — and  in  such  a  position  that 
the  screw  may  be  operated  by  the  thumb  and  second  finger,  and 
holding  the  pen  perpendicularly,  place  it  against  the  ruling- edge 
as  in  Figs.  45  and  46.  It  will  be  noted  that  in  this  position  the 
curvature  of  the  instrument  throws  the  pen  point  well  away  from 


9°  MECHANICAL   DRAWING. 

the  straight-edge  (this  is  important);  also  that  the  nibs  are  parallel 
to  the  ruling  edge;  maintaining  this  position,  move  the  pen 
along  the  ruler,  drawing  from  the  body,  with  just  sufficient  down- 
ward pressure  to  secure  smooth  and  even  contact  with  the  paper 
and  a  pressure  against  the  straight-edge  sufficient  to  maintain 
the  guide.  Varying  the  weight  of  line  by  increasing  or  decreas- 
ing the  width  between  the  nibs  by  means  of  the  thumb-screw 
operated  by  the  thumb  and  second  finger,  rule  a  number  of  lines 
and  note  their  contour.  Should  any  of  the  before-mentioned 
" faulty"  lines  result,  the  cause  can  be  recognized  and  the  fault 
eradicated. 

In  the  trial  for  the  very  fine  lines,  much  care  should  be  exer- 
cised not  to  screw  the  nibs  so  tightly  together  as  to  cause  them 

to  "flare"  out  at  the  point,  as  in  Fig.  47. 

|  With  the  pen  in  first-class  condition,  the  ruling 

\     1  I  of  lines  becomes  a  matter  of  practice.     Much  care 

\     I          /   must  be  exercised  to  maintain  the  original  position 

\\  I  /    of  the  pen — that  depicted  in  Figs.  45  and  46 — when 

\\/y      drawing  it  along  the  guide,  for  should  it  be  changed 
y/        by  throwing  the  handle  out  and  the  point  in  and 

FIG  47  a£amst  tne  guide,  the  ink  will  be  drawn  under  the 
guide  and  cause  a  blot ;  the  small  space  between  the 
straight-edge  and  the  pen-point  must  be  maintained.  Furthermore, 
should  the  position  of  the  pen  be  altered  in  any  way  changing 
the  original  space  between  the  point  and  the  guide,  the  line  will 
not  be  a  right  line — all  of  its  points  will  not  lie  in  the  same  direc- 
tion— and  as  mechanical  drawing  is  an  exact  art,  it  is  obvious 
such  lines  will  not  answer. 

Blotting  will  be  the  first  trouble  experienced  by  the  beginner, 
and  will  tend  to  augment  the  inaccuracy  of  his  lines;  in  trying  to 
secure  sufficient  space  between  the  pen-point  and  the  ruling-edge 
he  will  assume  a  position,  to  begin  with,  other  than  in  a  perpen- 
dicular, and  as  the  ruling  proceeds  and  the  hand  gets  farther 
from  the  body,  the  tendency  will  be  to  "  straighten  "  up  the  pen. 

While  a  perpendicular  position  of  the  pen  is  recommended, 
good  results  may  also  be  obtained  by  slightly  leaning  the  pen  in 


DRAWING    TOOLS  AND  MATERIALS. 


Joint 


the  direction  of  the  line,  keeping  it,  however,  in  a  vertical  plane 
parallel  with  the  straight-edge. 

89.  The  Compass. — Fig.  48.  The  compass — an  instrument 
for  drawing  circles — is  next  to  the  ruling-pen  in  importance,  and 
consists  of  five  pieces :  ( i )  the  com- 
pass proper,  (2)  the  pen- leg,  (3)  the 
pencil-leg,  (4)  the  extension-bar, 
and  (5)  the  center-point. 

All  the  joints  in  the  instrument 
should  have  a  firm,  even  bearing, 
and  should  be  free  from  all  binds 
and  play.  In  purchasing  a  new 
instrument,  all  the  parts  should  be 
placed  together,  the  joints  inspected, 
and  the  fits  noted.  With  the  pen-leg 
in  position,  the  instrument  should 
be  closed  and  the  center- point  set 
with  its  point  slightly  in  advance 
of  the  pen-point;  if  the  center- 
point  be  fashioned  with  a  shoulder, 
this  should  come  flush  with  the  pen- 
point.  When  the  center-point  is 
once  set  for  the  pen,  it  should  never 
be  changed;  the  pencil-point  must 
always  be  adjusted  to  the  center- 
point. 

The  remarks  on  the  ruling-pen 
apply  also  to  the  pen  of  the  pen-leg, 
the  pencil-point  will  be  treated  of  in 
the  discussion  of  lead-pencils  and 
leads.  Needle  point[ 

The  accuracy  of  the  construction 
of  the  tool  may  be  remarked  by 
closing  the  instrument  and  noting  the  position  of  the  points, 
which  should  lie  in  a  plane  perpendicular  to  the  axis  of  the  head 
and  passing  through  the  center  of  each  leg,  or  should  the  instru- 


Socket  J 


T.  screw 


92  MECHANICAL  DRAWING. 

ment  be  broken  at  the  knees  (to  the  same  degree)  and  the  points 
brought  together,  they  should  coincide. 

To  use  the  compass,  the  points  should  be  brought  to  the 
proper  adjustment  and  the  instrument  broken  at  the  knees — 
each  knee  to  the  same  degree — until  the  legs  of  the  tool  are  par- 
allel; now  place  the  center- point  on  the  point  about  which  the 
circle  is  to  be  drawn  and  press  it  "home"  if  the  point  is  "  shoulder'' 
fashioned,  otherwise  give  it  only  such  pressure  as  to  cause  the 
point  to  prick  the  paper  to  a  depth  sufficient  to  fix  it.  Do  not 
punch  large  holes  in  the  paper  or  the  work  will  be  inaccurate 
and  the  paper  unsightly. 

With  the  center-point  fixed,  erect  the  instrument  to  a  position 
such  that  a  line  dropped  from  the  center  of  the  heacj..will  be  pe£- 
pendicular  to  the  plane  of  the  paper,  and  if  the  adjustment  be 
correct,  .it  should  pierce  the  plane  of  the  paper  at  a  point  bisect- 
ing a  line  joining  the  two  points  of  the  compass.  From  this  first 
position,  slightly  incline  the  instrument  in  the  direction  in  which 
it  is  desired  to  draw  the  circle — usually  clockwise,  from  left  to 
right — and  with  a  downward  pressure,  only  sufficient  to  maintain 
the  center-point  where  fixed  and  to  secure  a  light  contact  between 
the  paper  and  the  ruling-point,  turn  the  instrument  in  the  direc- 
tion of  its  inclination  until  the  circle  is  described;  should  any  part 
of  the  line  be  dim  or  incomplete,  go  over  it  again  in  the  same 
manner  until  the  line  is  clean-cut;  never  reverse  the  order  and 
run  " backwards"  over  the  line. 

The  compass  should  be  used  only  for  the  larger-sized  circles, 
those  of  small  diameter  being  drawn  with  .the  bow-pen  or  bow- 
pencil.  When  a  circle  of  greater  diameter  than  the  instrument 
just  described  will  "span"  is  to  be  drawn  the  extension-bar 
must  be  used.  To  use  the  bar,  remove  the  ruling-point  and  insert 
the  shank  of  the  bar  in  the  socket  of  the  compass-leg  vacated  by 
the  shank  of  the  pen-leg,  and  the  latter  shank  in  the  socket  of  the 
extension- bar,  and  secure  all  joints;  next  break  the  knees  of 
the  instrument  until  the  two  legs  are  parallel,  then  pro- 
ceed as  above  described.  With  the  extension-bar  in  use,  a  line 
through  the  head  of  the  tool  and  perpendicular  to  the  plane  of 


DRAWING    TOOLS  AND   MATERIALS. 


93 


the  paper  will  pierce  the  paper  at  a  point  nearer  the  center-point 
than  the  ruling- point,  in  which  case  it  is  well  to  steady  the  long 
leg  with  the  free  hand;  when  possible,  however,  it  should  be  a 
"one-hand"  operation. 

The  compass  is  a  very  delicate  instrument  and  to  preserve  its 
accuracy  should  be  very  carefully  handled  and  cared 
for. 

90.  The  Dividers. — Fig.  49.  The  dividers  are 
used  to  lay  off  divisions  and  to  transfer  distances 
from  one  point  to  another,  as  in  copying  drawings, 
and  should  be  provided  with  a  hair-spring  adjust- 
ment for  very  fine  work.  This  instrument  is  even 
more  delicate  than  the  compass,  the  legs  being 
tapered  to  needle-points,  and  should  be  very  care- 
fully handled,  else  the  points  be  destroyed  and  the 
accuracy  of  the  tool  impaired.  Should  one  or  both 
of  the  points  become  broken  or  blunted,  they  can  g 
be  repointed  by  grinding  on  an  oil-stone. 

To  test  the  accuracy  of  the  instrument,  close  the 

id 

tool,  when  the  legs  should  be  of  equal  length  and    "= 
the  points  exactly  in  line  and  in  a  plane  perpendicu- 
lar to  the  axis  of  the  head  and  passing  through  the 
center  of  each  leg. 

To  use  the  dividers,  say  to  lay  off  a  given  line 
from  a  given  point,  hold  the  instrument  near  the 
top  with  the  thumb  and  first  finger  and  insert  the 
second  and  third  fingers  between  the  legs  of  the  tool. 
With  the  instrument  thus  in  hand  it  can  be  opened 
and  closed  with  the  one  hand.   Now  set  one  leg  with 
its  point  at  one  extreme  of  the  line  and  open  the 
dividers  to  a  width  closely  approximating  the  length 
of  the  given  line,  then  bring  the  width  between  the    Points 
points  to  exactly  equal  the  length  of  the  line  by  ad-      JTJG    49< 
justing  the  hair-spring;  next  transfer  the  tool  to  the 
given  point  and  place  one  point  exactly  on  it ;   then,  with  the 
other  leg  in  the  desired  position,  bring  its  point  in  contact  with 


o 


MECHANICAL  DRAWING. 


the  paper  and  either  mark  the  point  with  a  pencil  or  raise  the  in- 
strument, with  the  point  fixed,  until  the  leg  is  perpendicular  to 
the  plane  of  the  paper;  then  slightly  prick  the  surface.  In  no 
-case  should  the  prick-marks  puncture  the  paper,  as  it  renders  the 
paper  unsightly  and  the  work  inaccurate. 

The  dividers  are  to  be  used  where  the  work  is  comparatively 
large  and  the  lengths  variable.  The  joint  at  the  head  should  be 
quite  firm,  smooth,  and  even,  and  free  from  all  binds  and  play. 

91.  The  Bow-pen. — Fig.  50.  The  bow-pen  is  a  small  com- 
pass with  the  pen-leg  only,  the  joint  at  the  head  is  done  away  with, 

and  the  tool  so  fashioned  that  the 
legs  tend  to  spring  apart.  The  es- 
sentials of  a  good  bow-pen  are :  the 
temper  of  the  pen-point  should  be 
that  necessary  in  a  good  ruling -pen, 
the  spring  of  the  instrument  should 
be  quite  stiff,  the  threaded  member 
should  be  smoothly  and  truly  cut, 
and  the  thumb-screw  should  be 
capable  of  bringing  the  points  ex- 
actly together. 

To  adjust  the  instrument,  it 
should  be  closed  by  means  of  the 
thumb-screw  and  the  center-point 
set  slightly  in  advance  of  the  pen- 
point,  when,  if  the  instrument  be 
well  and  accurately  made,  the  points 
will  lie  in  line  with  each  other  and 
in  a  plane  passing  through  the  center  of  each  leg. 

To  facilitate  the  use  of  the  instrument  and  to  minimize  the 
"  wear  and  tear, "  instead  of  opening  and  closing  the  tool  by  means 
of  the  thumb- screw,  it  is  well  to  proceed  as  follows:  To  close  the 
pen,  hold  it  between  the  thumb  and  the  first  finger  of  the  right 
hand,  press  the  legs  together  by  means  of  the  left  hand,  and  with 
the  second  finger  of  the  right  hand  turn  the  knurled  nut  to  the 
proper  position.  To  open  the  instrument,  hold  it  as  for  closing, 


Ad  Justin 
screw 


Nibs!/    Needle  point 
FIG.  50. 


DRAWING    TOOLS  AND  MATERIALS. 


95 


.and  with  the  left  hand  "stay"  the  legs,  and  operate  the  nut  with 
the  thumb  of  the  right  hand;  when  the  nut  is  approximately  at 
the  desired  position,  permit  the  legs  to  spread  gently  until  the 
nut  prevents  further  movement.  This  operation  requires  much 
caution  to  prevent  the  legs  from  slipping  from  the  grasp  of  the  left 
hand  and  violently  springing  against  the  nut,  an  accident  several 
of  which  might  spoil  the  threaded  members  of  the  tool  and  render 
it  unfit  for  use. 

The  remarks  on  sharpening  the  ruling-pen  are  applicable  to 
the  sharpening  of  the  bow-pen;  as  a  special  caution,  however,  it 
may  be  added  the  center-point  should  be  removed  during  the 
operation. 


Adjusting 
screw 


Adjusting 
screw 


^Needle  point         Lead 

FIG.  51. 


The  bow-pen  should  always  be  used  on  small  work,  and  in 
fact  wherever  possible,  as  it  is  easier  of  manipulation  than  the 
•compass. 

92.  The  Bow-pencil. — Fig.  51.  The  bow-pencil  is  a  small 
vcompass  with  the  pencil-leg  only,  and  is  covered  by  the  remarks 


96  MECHANICAL   DRAWING. 

> 

on  the  bow -pen,  the  method  of  manipulation,  adjustment,  etc., 
being  the  same  for  both  tools. 

93.  The  Bow-dividers.— Fig.  52.     The  bow-dividers  are  small 
dividers  and  are  used  in  the  same  manner  as  the  other  two  bow 
instruments.     Other  specific  points  are  covered  by  the  remarks 
on  the  large  dividers. 

The  bow-dividers  are  used  for  small  work  or  wherever  possible, 
as  the  tool  has  the  advantage  over  the  larger  instrument  in  that 
it  is  not  liable  to  variation  when  once  set.  The  principal  use  of 
the  tool  is  for  the  laying  off  of  a  large  number  of  equal  divisions. 

94.  The  Box  for  Leads.— Fig.  41.     The  box  for  leads  should 
contain  leads  of  various  degrees  of  hardness  and  of  a  shape  and 
size  to  fit  the  instruments. 

95.  The  Care  of  Instruments. — Draughting    instruments    are 
instruments  of  precision   and   should  be  carefully  handled  and 
cared  for.     When  through   with  a  tool,   it  should  be  carefully 
cleaned  with  an  old  linen  or  cotton  rag  or  chamois-skin,  then  at 
once  placed  in  the  case.      Ink  or  other  foreign  substances  should 
never  be  allowed  to  dry  on  the  tools.     After  considerable  hand- 
ling, even  with  the  best  of  care,  a  slight  corrosion  will  make  its 
appearance,  particularly  on  the  ruling-pen;    this  is  due  to  con- 
tact with  the  moisture  of  the  hands  and  cannot  be  eliminated, 
save  to  a  degree. 

96.  Drawing-boards.  —  The    trade    has    a    large    variety    of 
drawing-boards,  adjustable  tables,  etc.,  on  the  market;   it  is  well, 
however,   for  the  beginner   to   first   provide  himself  with  some 
simply  constructed  board,    such   as  is  shown  in  Fig.   53.     The 
stock  should  be  of  well- seasoned,  clear,  soft  pine,  such  as  is  used 
for  pattern-making;  the  warping  tendencies  of  the  material  should 
be  minimized  by  saw-cuts  on  the  back  and  with  cleats  well  secured 
to  the  board.     The  top  face  should  be  given  a  smooth,   even 
finish  and  one  end  face  trued  and  jointed  to  this  face.     The 
planed  surface   is  the  "  working  -face "  and  the  jointed  edge  is 
the  "working-edge."      With  the  working-edge  at  the  left  hand 
and  the  working-face  up,  the  edge  farthest  from  the  observer  is 
the  top  of  the  board  and  that  edge  nearest  him  the  bottom.      The 


DRAWING    TOOLS  AND  MATERIALS. 


97 


student  should  fix  these  features  of  the  board  in  mind,  as  they 
will  be  used  in  further  discussions. 

97.  The  T-Square.— The  T-square  is  a  device  used  as  the 
basis  of  construction  for  all  accurate  drawing,  and  derives  its 
name  from  its  shape  and  use,  being  fashioned  like  the  letter  T, 
and  used  as  and  like  a  square.  Fig.  53  illustrates  the  ordinary 
T-square,  the  short  piece  being  the  "head"  of  the  square  and 
the  long  piece  the  "blade." 


FIG.  53. 

T-squares  are  made  of  various  materials,  the  more  common 
of  which  are  wood,  rubber,  amber,  and  metal,  and  with  solid 
and  adjustable  heads  and  various  attachments.  A  good  work- 
ing-square, one  answering  all  practical  purposes,  is  made  of 
straight-grained  hard  wood,  with  adjustable  head  and  a  blade 
with  amber  edges.  The  advantages  possessed  by  such  a  square 
are  its  greater  range  of  usefulness  because  of  the  adjustable  head, 
which  renders  it  more  than  a  simple  square,  and  the  advantage 
of  a  transparent  edge.  For  very  fine  work  a  metal  square  is 
the  best,  being  free  from  warping  tendencies  and  capable  of 
maintaining  the  most  accurate  straight  edge,  while  its  greater 
weight  makes  it  the  most  stable,  and  with  ordinary  care  slippage 
is  eliminated.  The  objections  to  the  metal  square  are  its  exces- 
sive first  cost  and  susceptibility  to  corrosion. 


98  MECHANICAL  DRAWING. 

In  purchasing  a  T-square,  the  size  of  the  drawings  to  be  made 
should  be  considered  and  a  square  selected  which  has  a  blade 
of  even  length  with  the  board  required  for  the  work.  The  work- 
ing-edge of  the  head  should  be  a  true  plane  surface,  jointed  with 
the  top  face;  the  blade  should  be  planed  true  on  all  sides  and  the 
faces  jointed. 

The  T-square  is  used  to  square  the  paper  on  the  drawing- 
board,  and  as  a  guide  for  the  ruling-points  for  drawing  horizontal 
lines,  and  for  the  triangles.  To  use  the  square,  place  it  on  the 
board  and  bring  the  working- edge  of  the  head  against  the  work- 
ing-edge of  the  board,  then  draw  along  the  working-edge  of  the 
blade  with  pen  or  pencil.  The  square  should  be  operated  with 
the  left  hand  and  the  drawing  done  with  the  right  hand,  if  right- 
handed.  The  head  of  the  square  should  be  held  near  the  center 
in  a  firm  though  not  a  strained  grasp,  and  having  drawn  a  line,  the 
square  may  be  shifted  up  or  down  and  any  number  of  parallel 
lines  drawn.  In  shifting  the  square,  much  care  should  be  exercised 
to  grasp  the  head  at  the  same  point  and  with  uniform  force, 
else  the  lines  will  not  be  parallel. 

The  blade  of  the  square  should  be  preserved  as  a  ruling-edge 
and  never  used  as  a  guide  for  a  knife  or  other  edged  tool  when 
cutting  paper;  if  limited  for  straight  edges,  one  edge  only  (the 
upper)  may  be  reserved  as  a  ruling- edge  and  the  other  edge  used 
as  a  u  cutting- edge."  Should  the  ruling-edge  become  untrue,  if 
the  square  be  a  wooden  one,  it  is  an  easy  matter  to  remove  and 
true  it  by  planing. 

98.  Triangles. — Fig.  53.  Having  provided  for  the  accurate 
ruling  of  horizontal  lines  with  the  T-square,  it  is  then  necessary 
to  provide  means  for  drawing  perpendicular  and  angular  lines, 
an  end  secured  by  the  use  of  triangles. 

Triangles  of  various  sizes  and  angles  may  be  had  of  wood, 
rubber,  amber,  metal,  and  a  number  of  other  materials,  of  which 
the  triangle  made  of  amber  is  the  most  desirable  because  of  its 
transparency  and  cleanliness.  The  objection  to  the  amber 
triangle  is  its  susceptibility  to  heat,  an  exposure  of  some  time 
to  the  sun's  rays  often  causing  the  triangle  to  warp;  however, 


DRAWMG    TOOLS  AND  MATERIALS.  99 

should  such  a  triangle  become  warped,  it  may  be  straightened 
by  reversing  it  and  again  exposing  it  to  the  sun.  The  objection 
cited  is  not  of  great  moment,  as  there  is  no  good  excuse  for  leaving 
one's  triangle  thus  exposed. 

As  to  the  size  of  a  triangle,  it  should  be  of  ample  dimensions 
for  the  work  in  hand;  one  engaged  in  constructing  large  drawings 
should  have  a  large  sized  triangle,  while  for  small  work  the  smaller 
sizes  are  more  convenient. 

The  angle  of  a  triangle  is  a  much  discussed  subject,  though 
draughtsmen  unite  in  recognizing  the  desirability,  almost  neces- 
sity, of  being  provided  with  angles  of  90°,  45°,  30°,  and  60°. 
The  manufacturer  meets  this  requirement  with  two  triangles: 
one  called  the  45°  triangle,  which  has  one  angle  of  90°  and  two 
angles  of  45°,  and  a  second  one  called  the  3o°-6o°  triangle,  or 
simply  the  60°  triangle,  which  has  an  angle  of  90°,  one  of  60°, 
and  one  of  30°;  with  these  two  triangles  and  the  T-square,  a 
circle  may  be  divided  into  twenty- four  equal  parts,  which  gives 
a  division  every  fifteen  degrees. 

That  a  drawing  may  be  exact,  it  is  necessary  that  the  triangles 
be  absolutely  true.  To  test  a  triangle  for  the  90°  angle,  place  it 
against  the  working-edge  of  the  T-square,  with  the  right  angle  up 
and  draw  through  a  given  point  a  vertical  line;  now  reverse  the 
triangle — turn  it  over  from  left  to  right  or  vice  versa — and  through 
the  same  point  draw  a  second  vertical  line;  if  the  two  lines  coin- 
cide, the  angle  is  correct,  otherwise  the  inaccuracy  will  show  as 
diverging  lines,  becoming  more  and  more  apparent  as  the  lines 
recede  from  the  point.  A  test  of  any  other  angle  may  be  made 
by  first  drawing  a  circle,  then  with  the  angle  against  the  working- 
edge  of  the  T-square  draw  a  line  through  the  center  of  the  circle 
and  intersecting  the  circumference;  now  reverse  the  triangle 
and  draw  a  second  line  through  the  center  of  the  circle  and  inter- 
secting the  circumference;  if  the  angle  is  correct,  a  horizontal 
line  through  one  of  the  points  of  intersection  on  the  circumference 
will  pass  through  the  other  point. 

Should  the  edges  of  a  triangle  become  nicked  or  otherwise 
injured,  or  should  the  angles  be  untrue,  the  triangle  is  practically 


ioo  MECHANICAL   DRAWING. 

useless  and  should  be  discarded,  though  a  skilled  workman  may 
eliminate  the  faults  by  planing. 

It  has  been  noted  that  the  T-square  should  be  used  for  all 
horizontal  lines;  the  T-square  and  triangles  should  be  used  for 
all  perpendicular  lines  and  all  other  lines  of  known  angles.  'The 
triangles  should  never  be  used  "free-hand"  (without  the  T-- 
square), as  such  a  procedure  is  time-consuming  and  inaccurate. 
As  a  last  word,  it  may  be  added,  never  use  a  triangle  as  a  guide 
for  a  knife-edge  in  cutting. 

99.  Irregular  Curves. — Fig.  72.     Irregular  curves  are  devices 
used  as  a  guide  for  drawing  all  arcs  other  than  the  arcs  of  circles. 
They  are  made  of  various  materials,  shapes,  and  sizes.     In  pur- 
chasing a  curve,  one  adapted  to  the  work  in  hand  should  be 
selected,  as  curves  to  fit  all  usual  figures  are  to  be  had.     The 
best  curve,  like  the  triangles,  is  one  made  of  amber. 

The  manner  of  using  the  curve  is  set  forth  in  Sect.  197,  and 
requires  much  practice  to  attain  proficiency. 

100.  The  Architect's  Scale. — As  all  mechanical  drawings  are 
drawn  proportional  to  the  object,  it  is  necessary  to  "lay  off" 
the  drawing  to  scale.     Scales  for  this  purpose  may  be  had  of 
various  materials,  principal   among  which   are  ivory,  boxwood, 
and  metal,  and  graduated  to  any  denomination.     There  are  two 
denominations  in  general  use,  (i)  a  graduation  of  tenths  of  an 
inch,  and  (2)   a  graduation  of  sixteenths  of  an  inch.     A  scale 
graduated  in  tenths  inches  is  called  the  "Engineer's  Scale,"  and 
the  scale  with  y1/'  divisions  is  called  the  "Architect's  Scale." 

The  engineer's  scale  is  used  mostly  in  government  work, 
mapping,  surveys,  etc.,  while  the  architect's  scale  is  the  one  of 
general  usage,  the  common  scale  being  of  boxwood  and  known 
as  the  "architect's  tringular  scale,"  the  word  "triangular"  signify- 
ing three- sided  (Fig.  54). 

The  ordinary  architect's  scale  contains  eleven  separate  scales: 
(i)  A  full- sized  scale  which  is  i  foot  in  length,  the  foot  is  gradu- 
ated into  inches,  and  the  inches  into  sixteenths  inches.  This 
scale  is  designated  by  the  figure  16  under  the  6-inch  division 
of  the  scale,  or  in  some  cases  at  one  end  of  the  scale.  In  using 


DRAWING    TOOLS  AND  MATERIALS.  101 

this  scale,  the  drawing  is  laid  off  inch  for  inch  of  the  object  drawn. 
The  next  scale  for  drawings  is  a  scale  of  three-fourths  size,  or 
9"  =  i'.  To  construct  a  drawing  to  this  scale,  the  dimensions 
are  reduced  mentally,  or  otherwise,  to  three- fourths  of  the  original 
and  the  drawing  laid  out  with  the  full-size  scale.  Half- sized  draw- 
ings, or  a  scale  of  6"  =  i',  which  is  the  next  usual  scale  for  draw- 


£A  \AA\\\\\Av\\v\\\x\\v\Av\\AAA\v\Ax\\v\A\\\AAv\\N\AA\Av\ 


FIG.   54. 

ings,  are  constructed  in  a  similar  manner.  Should  it  become 
necessary  to  lay  off  a  division  smaller  than  TV'»  say  -£$"  or  ^", 
this  may  be  done  by  using  the  full-sized  scale  and  bisecting  the 
TV"  division  with  the  eye  for  thirty  seconds  and  quartering  the 
yV'  division  for  sixty- fourths;  with  a  little  practice  very  accurate 
divisions  may  be  made. 

(2)  The  next  scale  is  a  scale  of  one-fourth  size,  or  3"  =  !'. 
This  scale  is  found  on  the  "flat"  of  the  tool  adjacent  to  the  full- 
sized  scale,  on  the  zero  end,  and  is  designated  by  the  figure  3 
stamped  at  the  end.     A  length  of  3'  is  given  on  the  scale,  the 
divisions  being  marked  in  the  groove.     One  foot  of  the  scale 
is  graduated  into  inches  and  these   into  halves,  quarters,  and 
eighths,  each  division  on  the  scale  representing  f ".     For  dimen- 
sions smaller  than  J",  approximations  may  be  made  as  already 
described. 

(3)  A  scale  of  one-eighth  size,  or  ij"  =  i',  is  the  next  smaller 
scale,  and  is  given  on  the  same  flat  with  the  3"  scale,  the  designing 
figure,  ij,  being  at  the  opposite  end.     This  scale  is  graduated  to 
5'  in  length,  the  figures  being  stamped  on  the  flat  of  the  rule; 
i'  is  graduated  into  inches  and  these  into  halves  and  quarters. 
Smaller  divisions  may  be  approximately  as  above. 

With  the  foregoing  explanation  as  a  key,  and  remembering 
that  when  viewing  a  scale,  if  it  is  on  the  right-hand  end  of  the  rule 


102 


MECHANICAL  DRAWING. 


the  foot  divisions  are  stamped  in  the  groove,  and  if  on  the  left- 
hand  end,  the  figures  are  on  the  flat  of  the  rule,  the  remaining 
eight  scales  may  be  interpreted.  They  are: 

(4)  Scale  of    i"  =  i',  =TV  size,  smallest  divisions  of  which  =  £". 


(5) 
(6) 
(7) 
(8) 

(9) 
(10) 


<.  i      \rt T/  _  i        it 

4     :~  I  >  -  t* 

«         £    //  _  T/         1  « 

~16           A  )  1T3" 

«      3  /'  _  T'  1        « 

"5^     -1  >  —  T7JT 


=  ¥'• 


_  T 
—  1 


=  1' 


The  scales  given  are  the  usual  scales;  however,  should  an  odd 
scale  be  required,  one  may  be  constructed  as  follows:  Let  it  be 
required  to  divide  i"  into  sixths  (A,  Fig.  55).  The  nearest  division 


FIG.    55. 

given  on  the  scale  is  the  i"  division  of  the  full- sized  scale;  to  use 
this,  erect  a  perpendicular  at  one  extremity  of  the  i"  line,  and 
with  an  inch  division  of  the  scale  on  the  other  extreme,  radiate 
the  scale  from  this  latter  point  until  a  division  ij",  or  f"  away 
from  the  inch  division,  coincides  with  the  perpendicular,  or,  better, 
with  the  perpendicular  drawn,  take  a  radius  of  ij"  on  the  bow- 


DRAWING    TOOLS  AND  MATERIALS.  103 

pencil,  and  with  the  free  end  of  the  line  as  a  center,  describe  an 
arc  intersecting  the  perpendicular  in  a  point;  joining  this  point 
and  the  center  gives  a  line  ij"  long.  Now  on  this  line  lay  off 
\"  divisions,  which  gives  six  divisions;  dropping  perpendiculars 
through  these  six  points  of  division  to  the  i"  line  will  give  six 
equal  divisions  on  the  line,  sixths  of  an  inch.  "/*"  illustrates  a 
3"  length  divided  into  seven  equal  lengths  by  a  similar  method. 

The  mistake  should  not  be  made  of  attempting  to  use  the 
scales  f"  =  i',  J"  =  i',  etc.,  for  laying  out  three  quarter-  and  half- 
sized  drawings  respectively,  as  an  inspection  of  the  scale  will 
show  the  graduations  to  then  read  J",  }",  -&',  2Y'  for  the  f" 
scale  and  J",  J",  -jV'  f°r  tne  J"  scale,  which  divisions  are 
odd  and  seldom  used.  Any  scale  may  be  doubled,  tripled, 
quadrupled,  etc.;  for  example,  double  the  i"  =  i'  scale;  this 
changes  the  smallest  division  from  J"  to  J"  and  gives  a  scale  of 
2"  =  i',  or  one-sixth  size. 

The  architect's  scale  is  one  of  the  "fine"  tools,  the  gradu- 
ations being  accurate,  and  in  using  it  much  care  should  be  exer- 
cised to  preserve  the  sharpness  of  its  edges  and  the  clearness  of 
the  graduations. 

To  properly  use  the  scale,  lay  it  flat  on  the  paper,  with  the 
scale  in  use  from  the  body  and  in  good  light,  and  lay  off  the 
divisions  with  a  fine- pointed  pencil  or  metal  point,  being  careful 
not  to  bring  a  pressure  on  the  pencil  sufficient  to  dent  the  surface 
of  the  paper,  or  using  the  metal  point,  do  not  puncture  the  paper 
to  a  depth  which  would  mar  the  surface.  Do  not  use  metal 
points  on  the  scale,  or  use  it  as  a  guide  for  ruling  or  cutting. 

10 1.  Thumb-tacks.  —  "Thumb-tack"  is  the  name  given  a 
large- headed  small  tack  specially  designed  for  temporarily  fasten- 
ing paper  or  cloth  to  wood;  they  are  used  in  drawing  to  fasten 
the  drawing-paper  or  tracing- cloth  to  the  drawing-board.  The 
one  essential  of  a  satisfactory  thumb-tack  is  that  it  have  a  head 
of  sufficient  area  to  prevent  it  tearing  through  the  paper  or  cloth, 
and  that  it  be  so  fashioned  as  not  to  be  an  obstacle  to  the  free 
movement  of  the  T-square  and  triangles  over  the  surface  of  the 
drawing. 


I(H  MECHANICAL   DRAWING. 

The  ordinary  tack-head  is  about  ^y  to  ~^ff  thick  and  is  more 
or  less  troublesome;  to  minimize  the  difficulty,  3-oz.  or  4-oz. 
common  tacks  may  be  used,  driven  flush  with  the  surface  of  the 
drawing-board  ;  the  objection  to  this  practice  is  that  the  small 
head  of  such  a  tack  is  not  of  sufficient  area  to  retain  the  paper. 
As  the  student  becomes  more  and  more  expert  in  the  manipula- 
tion of  his  tools,  the  average  thumb-tack  ceases  to  be  troublesome. 

102.  Pencils  and  Leads. — A  drawing  is  always  first  con- 
structed in  pencil,  then  finished  in  ink.  "What  is  the  best  draw- 
ing-pencil" is  a  question  on  which  every  draughtsman  has  his 
own  private  opinion.  The  degree  of  hardness  of  lead  best  adapted 
to  the  work  is  largely  dependent  upon  the  nature  of  the  surface  to  be 
penciled  on;  generalizing,  paper  is  best  worked  with  a  hard 
lead  and  cloth  with  a  soft  lead.  For  paper  a  6-H  (trade  name) 
pencil  is  recommended,  while  for  cloth  good  results  are  obtained 
with  a  2-H  pencil. 

Penciling  a  drawing  is  like  laying  the  foundation  of  a  house: 
it  is  the  basis  upon  which  the  building  is  done,  and  any  inaccuracy 
in  the  penciling  will  appear  in  the  finished  drawing.  In  pen- 
ciling all  lines  are  made  practically  of  the  same  weight,  which 
weight  is  a  line  just  sufficiently  heavy  to  stand  out  clear  and 
distinct. 

To  secure  nice,  clean-cut  lines,  the  pencil-point  should  be 
given  careful  attention,  never  being  allowed  to  become  rough  or 
dulled.  There  are  several  styles  of  points  given  leads,  the  three 
most  prominent  being  (i)  the  round  or  needle  point,  (2)  the  flat 
or  chisel  point,  and  (3)  the  bevel  or  one-sided  point. 

(i)  The  round  or  needle  point  is  the  most  common  and  has 
the  widest  range  of  usefulness,  being  fairly  well  adapted  for  all 
ordinary  drawing;  it  is,  however,  especially  convenient  for  mark- 
ing points  and  for  all  free-hand  work,  such  as  free-hand  lettering, 
dimensioning,  etc.  To  fashion  the  needle-point,  begin  at  a 
point  about  ij"  from  the  end,  and  with  a  sharp  knife  bring  it 
(the  pencil  end)  to  a  neat  and  true  cone,  from  the  apex  of  which 
the  lead  projects  about  J";  now  bring  the  lead  to  a  uniformly 
tapered  needle-point,  and  finish  by  spinning  the  pencil-point  in  a 


DRAWING    TOOLS  AND  MATERIALS.  105 

cloth  held  about  it,  thus  removing  all  roughness  and  producing  a 
fine,  smooth  point.    This  pointing  of  the  lead  is  best  accom- 


FIG.  56 

plished  with  the  aid  of  a  piece  of  fine  sandpaper  or  emery-cloth 
(the  latter  is  the  better),  by  drawing  the  pencil-point  over  the 
surface  of  the  paper  or  cloth  and  turning  it  at  the  same  time 
until  ground  to  a  point.  In  any  case  the  point  should  be  "pol- 
shed  off"  with  a  rag,  as  described. 

To  facilitate  such  use  of  sandpaper  or  emery-cloth,  it  should 
ibe  stretched  over  a  flat  surface  and  securely  fastened.  A  good 
arrangement  is  obtained  by  making  a  small  paddle  of  wood  and 
gluing  the  abrasive  to  its  faces,  or,  better,  as  the  paper  and  cloth 
soon  become  dull  and  unfit  for  further  use  (in  the  order  named), 
it  is  well  to  make  a  pad  of  the  material,  then  as  one  sheet  becomes 
dulled  it  can  be  removed  and  a  new,  sharp  sheet  is  presented. 

(2)  The  flat  or  chisel-pointed  lead  is  restricted  to  the  drawing 
of  very  fine  lines,  and  is  for  accurate  work,  being  especially 
adapted  to  the  graphic  solution  of  problems.  To  fashion  the 
chisel- point,  begin  at  a  point  about  i£"  from  the  end,  and  with  a 
sharp  knife  bring  two  sides  to  a  smooth  and  even  bevel,  with  the 
lead  extending  about  J"  from  the  end  of  the  bevel;  next  bring 
the  remaining  faces  of  the  pencil  to  a  smooth  and  true  bevel  to 
within  about  i"  of  the  end  of  the  lead,  and  then  with  knife  or 
pad  continue  the  first  two  bevels  until  the  lead  is  very  sharp,  and 
finish  with  a  cloth,  slightly  rounding  (lengthwise)  the  point. 


106  MECHANICAL  DRAWING. 

To  have  the  needle  and  chisel-points  always  at  hand,  it  is  well 
to  " double  end"  the  drawing-pencil,  one  style  point  on  each  end. 
The  two  points  described  are  primarily  for  the  pencil-point  only, 
though  leads  used  in  the  compass  and  bow-pencil  may  be  simi- 
larly fashioned,  in  which  case  the  chisel-point  should  be  adjusted 
in  the  instrument  with  a  broad  side  next  to  the  center-point. 

(3)  The  bevel  or  one  sided  point  is  especially  designed  for  the 
lead  points  used  in  the  instruments,  and  is  fashioned  by  beginning 
at  a  point  about  \"  from  the  end  of  the  lead,  and  with  knife  or 
pad  making  a  smooth,  true  bevel  on  one  side  only  and  entirely 
across  the  lead;  the  point  is  then  finished  with  a  cloth.  The 
lead  is  adjusted  in  the  tool  with  the  center  of  the  straight  side 
next  to  the  center-point. 

When  ruling,  the  pencil  should  be  held  in  a  manner  similar 
to  that  described  for  the  ruling-pen,  and  especial  attention  given 
to  maintaining  one  position  throughout,  that  the  lines  may  be 
exact,  right  lines. 

103.  Pens  and  Penholders.— The  selection  of  a  pen  is  largely  a 
matter  of  preference  for  some  particular  brand,  though  the  "style" 
of  pen  is  determined  by  the  nature  of  the  work  to  be  done;  for 
etching  and  for  all  small,  fine  work  a  lithographic  crow-quill  pen 
is  the  best,  for  all  ordinary  work,  as  lettering  and  sketching,  any 
ordinary  fine-pointed  pen  will  answer,  and  for  heavy  work,  as 
large  lettering  for  titles,  a  ball- pointed  or  other  heavy  pen  is  recom- 
mended. From  the  first  to  the  last  are  many  points  of  various 
degrees  of  fineness,  and  that  pen  best  suited  to  the  work  in  hand 
is  readily  determined  after  a  short  experience. 

The  one  requisite  for  a  good  penholder  is  that  it  be  of  a  size 
and  shape  to  fit  the  hand  without  cramping;  avoid  all  very  small 
penholders.  The  pen  should  be  firmly  secured  in  the  holder. 

The  beginner  should  provide  himself  with  at  least  three  pen- 
points:  (i)  a  crow-quill,  (2)  a  common  writing-pen,  and  (3)  a 
ball-pointed  pen;  with  these  he  will  be  equipped  for  this  course 
and  for  all  usual  drawing.  A  new  pen  will  always  prove  more  or 
less  troublesome,  as  the  ink  will  not  flow  freely,  and  requires  to 
be  "broken  in." 


DRAWING    TOOLS  AND  MATERIALS.  107 

The  pen  is  one  of  the  draughtsman's  tools,  and  as  such  should 
receive  proper  care  and  attention;  do  not  treat  it  roughly  because 
it  is  "  just  a  common  pen"  and  is  cheap.  To  have  a  good  pen  it 
must  be  first  broken  in,  then  preserved.  The  pen  should  always 
be  carefully  wiped  with  a  rag  free  from  lint  or  fuzz  before  laying 
it  aside;  never  lay  a  pen  down  without  wiping  it  off. 

104.  Erasers. — In  constructing  a  drawing  a  large  number  of 
pencil-lines  are  drawn  which  are  not  to  appear  on  the  finished 
drawing  and  must  be  erased;  also,  errors  may  be  made  in  inking- 
in  a  drawing,  necessitating  an  erasure;   alterations  on  a  finished 
drawing  may  be  desired,  which  involves  erasures,  etc.;  thus  it  is 
that  a  drawing  outfit  is  incomplete  without  some  means  of  erasing 
pencil  and  ink  lines. 

An  outfit  should  contain  at  least  two  erasers:  (i)  a  pencil 
eraser,  and  (2)  an  ink  eraser;  a  combination  eraser,  one  end 
for  pencil  and  one  end  for  ink,  will  answer.  The  pencil  eraser 
should  be  of  soft  rubber  and  possessed  of  a  property  which  enables 
it  to  "take  hold"  on  the  paper;  an  eraser  that  is  hard,  gritty,  or 
that  has  a  glazed  surface  is  unfit  for  erasing  pencil-lines. 

An  ink  eraser  should  be  hard  and  gritty,  but  should  be  pliable. 
All  erasers  after  a  time  become  hard  and  stiff  and  lose  their 
erasive  properties;  an  eraser  should  be  much  handled  and 
"worked." 

For  simply  cleaning  a  sheet  of  paper,  a  third  eraser  known  as 
a  "  sponge  eraser  "  is  very  efficient  and  is  a  valuable  addition  to 
an  outfit. 

105.  Ink. — Until  recent  years  it  was  customary  for  draughts- 
men to  prepare  their  own  ink  from  a  stick  of  India  or  Chinese 
ink,  by  rubbing  it  in  a  specially  designed  saucer  containing  a 
small  quantity  of  water.    A  very  superior  ink  is  thus  produced, 
but  the  operation  is  quite  laborious  and  time-consuming. 

The  market  of  to-day  affords  a  number  of  prepared  inks,  and 
from  these  a  draughtsman's  ink  is  usually  selected.  There  are 
but  two  colors  of  ink  much  used  in  drawing:  (i)  black  ink,  and 
(2)  red  ink. 

Black  drawing-ink  differs  from  ordinary  writing-fluid  in  that 


lo8  MECHANICAL  DRAWING. 

it  is  heavier  and  less  fluent.  It  is  a  form  of  carbon  in  suspension, 
and  when  applied  to  paper  or  cloth,  leaves  a  deposit  of  carbon 
which  is  at  once  fixed  and  distinct.  Drawing-ink  is  easily  erased 
because  of  this  deposit,  as  it  is  "on"  the  paper  and  not  "in"  it 
if  the  paper  be  a  good  drawing-paper 

A  good  drawing  ink  has  the  carbon  in  perfect  suspension,  is 
smooth  and  even  flowing,  with  no  granular  precipitation  what- 
ever, and  will  produce  clear  and  lasting  lines. 

The  red  ink  is  more  fluid  than  the  black  drawing- ink  and 
requires  great  caution  in  its  use,  as  it  has  a  tendency  to  "run" 
from  the  pen  onto  the  paper  and  under  the  edge  of  the  T-square 
and  triangles  and  cause  blots.  If  a  drawing  is  to  be  permanent, 
red  "drawing  ink"  should  be  used  (not  a  writing-fluid),  as  this,  like 
the  black  ink,  has  the  pigment  in  suspension  and  leaves  a  deposit 
on  the  paper.  The  objection  to  the  use  of  red  ink  on  drawings 
is  that  all  red  ink  is  more  or  less  susceptible  to  the  light  and  in 
time  will  fade;  also,  it  is  less  opaque  than  the  black  ink  and  is 
not  "printable,"  save  to  a  degree,  a  fact  which  is  sometimes 
taken  advantage  of  in  blue  printing  to  render  center  lines  and 
dimension  lines  lighter  than  lines  of  the  drawing. 

1 06.  Rag  and  Blotter. — A  rag  for  cleaning  instruments  and 
wiping  pens  should  be  free  from  lint  and  fuzz  and  very  absorp- 
tive.    The  cloth  most  acceptably  fulfilling  these  requirements  is  an 
old  linen  or  muslin  rag. 

An  ordinary  blotter  is  an  often  needed  article  when  drawing; 
not  to  blot  the  lines,  however,  as  these  must  be  allowed  to  dry, 
but  to  assist  in  removing  blots. 

107.  Horn  Center. — The   horn   center   is   a   device   of   some 
transparent   material,  designed  to  be  fixed  over  a    center-point 
and  to  receive  the  needle-point  of  the  instrument  when  drawing 
a  large  number  of  concentric  circles,  thus  avoiding  a  puncture 
of  the  paper.      Such   marring   of  the  surface  of  a  drawing  is 
avoided  without  the  use  of  a  horn  center  with  ordinary  care, 
and  they  are  only  needed  when  a  handsome,  line- shaded  drawing 
is  attempted. 

108.  Section-liners. — "Section -liner"    is    the    name    given    a 


DRAWING    TOOLS   AND  MATERIALS.  109 

machine  for  accurately  cross-hatching  surfaces.  It  is  a  convenient 
but  costly  device,  and  as  cross-hatching  is  done  in  a  number  of 
abbreviated  forms  and  is  not  required  to  be  accurate  a  section- 
liner  is  not  a  necessity  to  the  draughtsman. 

109.  Erasing-shields.  —  This  is  a  device  of  thin  material, 
amber  and  various  metals,  with  various  shaped  and  sized  open- 
ings, designed  to  mat  out  portions  of  a  drawing  to  be  erased. 

no.  Protractors. — A  protractor  is  a  device  graduated  in 
degrees,  and  is  used  in  laying  off  angles  not  obtainable  with  the 
triangles  and  T-square.  Protractors  may  be  had  of  various 
materials,  the  best  being  of  metal. 

in.  Scale-guard. —  A  scale-guard  is  an  attachment  for  the 
triangular  scale  and  is  of  use  when  one  scale  only  is  in  constant 
use,  as  it  enables  the  draughtsman  to  keep  that  scale  always 
before  him. 

112.  Proportional    Divider. — The    proportional    divider    is    a 
double-ended     pair    of    dividers    provided    with    an    adjustable 
clamp  which  enables  the  draughtsman  to  set  one  end  of  the  tool 
at  full  size,  and  by  means  of  the  adjustment  the  other    end  is 
made  to  be  some  proportional  size,  as  J  size,  \  size,  etc.     Their 
use  is  obvious. 

113.  Erasing-knives. — Erasing-knives  are  a  valuable  addition 
to  a  drawing  outfit;    but  as  most  draughtsmen  are  possessed  of  a 
pocket-knife,  such  a  knife,  well  sharpened,  answers  all  practical 
purposes. 

114.  Soapstone    Pencil. —  Soapstone  is  used  to  resurface  the 
surface  of  tracing- cloth  after  an  erasure  has  been  made. 

115.  Paper. — Having    discussed    ways    and    means    of    con- 
structing  drawings,  it    now  becomes   necessary    to   select   some 
material  on  which  to  construct  the  drawings.     For  this  purpose 
any  smooth  surface  will  answer,  shopmen  often  using  the  shop 
floor,  a  board,  the  wall,  a  blackboard,  etc.,  for  rough,  free-hand, 
temporary  sketches;    however,  the  draughtsman's  work  is  sup- 
posed to  have  finish,  accuracy,  to  be  permanent,  in  short,  to  be 
valuable,  and  for  his  purposes  the  field  is  limited  to  cloth  and  to 
paper. 


no  MECHANICAL  DRAWING. 

All  sketches,  preliminary  draughts,  etc.,  are  nearly  always 
made  on  paper,  cloth  being  reserved  for  the  finished  drawing, 
especially  when  the  drawing  is  to  be  duplicated,  as  by  blue  print- 
ing. 

The  selection  of  the  quality  of  paper  and  its  dimensions  is 
determined  by  the  nature  of  the  work  to  be  done.  Broadly 
speaking,  if  the  paper  be  intended  for  preliminary  work,  a  cheap, 
low-grade  paper  will  answer;  while  if  the  work  is  to  be  a  finished 
and  permanent  article,  an  expensive,  high-grade  paper  should 
be  used.  For  the  greatest  permanency,  a  high-grade  paper 
mounted  on  cloth  is  recommended. 

A  good  drawing-paper  should  be  of  a  color  to  cause  the  lines 
to  stand  out  sharply  (in  contrast)  and  the  color  should  be  perma- 
nent, the  light  having  no  effect  upon  it.  It  should  have  a  hard, 
smooth,  and  even  surface,  taking  pencil  and  ink  lines  sharply,  the 
latter  without  any  tendency  to  spread  or  blot,  and  should  take 
erasures  to  quite  an  extent.  Added  to  this,  it  is  quite  desirable, 
for  all  usual  purposes,  that  the  paper  should  have  some  body — 
be  rather  stiff — thus  minimizing  any  tendency  to  wrinkle  or  to 
buckle. 

The  paper  most  nearly  fulfilling  the  above  requirements 
is  a  pure  rag  or  linen,  hot-pressed  paper,  white  in  color.  It 
should  be  understood  this  applies  only  to  paper  for  good,  per- 
manent, inked  drawings;  for  pencil  work  and  work  that  is  to  be 
traced,  any  paper  that  has  body  and  will  take  erasures  will  answer. 

As  has  already  been  noted,  the  size  of  the  paper  is  determined 
by  the  size  of  the  work  to  be  done.  Paper  is  furnished  by  the 
trade  in  two  forms,  (i)  sheets  and  (2)  in  rolls,  the  dimensions 
being  for  sheets: 

Medium 17^X22" 

Royal i9"X24" 

Imperial 22"  X  30" 

Double  elephant 27"  X  40" 

While  rolls  of  almost  any  length  and  from  2  ft.  to  6  ft.  wide 
may  be  had,  only  the  finer  grades  of  paper  are  offered  in  sheet 


DRAWING   TOOLS  AND  MATERIALS.  in 

form,  though  any  roll  paper  will  be  cut  to  order.  Sheet  paper  is 
sold  at  so  much  per  sheet,  ream,  and  quire;  roll  paper  at  so  much 
per  yard  of  certain  width,  and  some  grades  by  the  hundred 
pounds. 

In  draughting-rooms,  where  all  work  is  traced,  it  is  customary 
to  use  roll  paper  of  suitable  width,  the  draughtsman  tearing  off 
such  amounts  as  needed. 

If  sheet  paper  is  to  be  used,  that  size  should  be  selected  which 
reduces  waste  to  a  minimum.  For  example,  let  it  be  required  to 
furnish  paper  to  cut  into  g"xi2"  sheets;  the  Royal,  i9"X24", 
sheet  will  be  found  to  four- fold  into  9j"Xi2",  giving  four  sheets 
of  these  dimensions,  each  sheet  having  J"Xi2"  waste,  an  amount 
which  when  divided  in  two  will  give  J"  waste  at  the  top  and 
bottom  of  the  sheet,  sufficient  to  cut  out  the  thumb-tack  holes; 
this  is  the  size  of  paper  required  for  the  drawings  of  this  course. 

116.  To  Make  Erasures  on  Paper. — The  quality  of  the  paper 
being  right,  the  labor  of  neatly  removing  pencil  lines  is  directly 
dependent  upon  the  character  of  the  penciling.  For  the  best 
results,  the  penciling  should  be  done  with  a  fine-pointed,  hard 
lead,  and  the  lines  made  very  light,  just  sufficiently  heavy  to  be 
clean-cut  and  clear.  To  do  this  the  pencil  must  be  handled  very 
lightly  and  no  crease  made  in  the  surface  of  the  paper,  a  case 
wherein  the  pencil-mark  may  be  removed,  but  not  the  crease. 
To  make  the  erasure,  lightly  rub  the  pencil  eraser  over  the  line 
until  it  disappears,  and  then  with  a  cloth  dust  off  the  paper. 
When  working  on  high-grade  paper,  this  last  item  is  of  great  im- 
portance, for  if  the  paper  be  not  dusted  and  the  erasure  be  per- 
mitted to  remain  on  the  surface,  it  will  soon  become  ground 
into  the  paper  and  cannot  then  be  clearly  removed. 

To  make  ink  erasures  on  paper,  it  is  best  to  use  the  ink  eraser 
and  with  considerable  pressure  rub  the  line  to  be  removed  until 
it  is  quite  indistinct,  then  dust  off  the  surface,  and  finish,  as  above 
described,  with  the  pencil  eraser  and  again  dust  off;  such  a 
treatment  well  applied  should  leave  a  surface  uniform  with  the 
remainder  of  the  sheet,  and  one  that  will  again  take  ink  without 
.any  resurfacing  of  the  spot.  If  the  line  to  be  removed  be  a  heavy 


H2  MECHANICAL  DRAWING. 

one,  it  will  facilitate  the  operation  if  the  erasing-knife  be  first 
applied.  To  do  this,  hold  the  knife-blade  in  a  plane  perpen- 
dicular to  the  line  and  lightly  scratch  the  ink  deposit  until  it 
becomes  quite  dim,  then  proceed  with  ink  and  pencil  erasers. 
Great  care  must  be  exercised  when  using  the  knife  not  to  dig 
into  the  paper  or  to  scuff  the  surface. 

117.  Profile  and  Cross-section    Paper. — These   are   specially 
ruled  papers,  much  used  for  plotting  and  for  sketch-work. 

118.  Tracing-paper.  —  Tracing-paper   is    comparatively    thin 
paper,  specially  treated  to  render  it  transparent,  and  is  used  as 
a  substitute  for  tracing-cloth,  because  of  its  lesser  cost.    Trans- 
parent profile  and  cross- section  paper  may  be  had  of  the  trade. 

In  most  oaper  there  is  a  right  and  a  wrong  side  to  it;  that  side 
which  presents  the  smoothest  surface  should  be  used. 

119.  Blue-print  Paper. — This  is  a  specially  prepared  paper 
used  for  reproducing  drawings,  for  making  blue-prints,  a  white 
line  on  a  blue  background.      The  paper  is  coated  with  a  solution 
of  certain  salts  which  are  susceptible  to  the  sun's  rays,  an  expos- 
ure thereto  causing  the  prepared  surface  to  undergo  a  change. 

Prepared  paper  may  also  be  had  which  will  give  blu ;  lines  on 
a  white  background,  and  several  other  contrasts. 

Blue-print  paper  is,  comparatively,  a  cheap  commodity,  and  is 
supplied  by  the  trade  in  various  qualities,  sizes — us  ally  in  lo-yd. 
rolls  of  variable  widths — and  degrees  of  sensitiveness,  from  the 
extra-rapid  printing  to  the  five-  and  ten-minute  paper. 

The  paper  can  be  bought,  ordinarily,  cheaper  than  it  can  be 
made,  and  when  thus  obtained  is  of  uniform  quality;  however, 
should  it  be  desired  to  prepare  some  paper,  the  following  formula 
is  recommended:  Dissolve  5  oz.  (avoirdupois)  of  red  prussiate 
of  potash  in  32  oz.  (fluid)  of  rain-water,  permit  it  to  stand  for 
two  or  three  days,  then  filter.  When  ready  to  use,  for  every 
200  sq.  ft.  of  paper  dissolve  i  oz.  (avoirdupois)  of  citrate  of 
iron  and  ammonia  in  4^  oz.  (fluid)  of  rain-water  and  mix  the 
two  solutions  in  equal  volumes.  Any  paper  with  a  smooth, 
hard  surface  may  be  used  and  the  solution  applied  with  a  sponge, 
care  being  taken  to  give  the  surface  a  smooth  and  even  coating, 


DRAWING    TOOLS  AND  MATERIALS.  ^3 

or  the  paper  may  be  floated  on  a  basin  filled  with  the  solution 
and  thus  coated.  If  both  sides  are  to  be  prepared  for  printing, 
the  paper  can  be  dipped  in  the  solution.  After  the  surface  has 
been  coated,  the  paper  should  be  hung  up  in  a  dark  place  to 
dry,  and  when  dry  is  ready  for  use.  It  is  obvious  the  paper 
must  be  protected  from  the  sunlight  until  ready  to  use. 

The  above  solution,  for  the  best  results,  should  be  given  three 
or  four  minutes  in  a  bright  sunlight. 

Linen  fabric  is  also  prepared  for  printing  purposes. 

120.  Tracing-cloth.— Tracing-cloth,  or  tracing-linen,  is  smooth, 
thin,  linen    cloth  which  has  been  treated  with  "size,"  one  side 
being  finished  with  a  glazed  surface  and  the  other  in  the  rough. 
It  is  very  transparent  and  is  used  for  tracing  drawings,  the  com- 
mon practice  of  the  day  being  to  trace  all  permanent  work,  the 
cloth  being  less  destructible  than  paper,  and  being  transparent, 
the  drawing  can  be  reproduced  by  blue-printing. 

"Which  side  of  the  cloth  is  the  best  for  use"  is  a  much  dis- 
cussed question,  each  side  having  its  advantages.  The  smooth 
side  takes  erasures  the  better,  that  is,  erasures  may  be  made  on 
this  side  more  easily  than  on  the  rough  side;  the  smooth  side  is 
a  trifle  the  better  for  free-hand  work,  such  as  lettering,  dimen- 
sioning, etc.,  but  when  drawings  are  made  on  this  surface,  the 
cloth  has  a  tendency  to  curl  up,  a  very  troublesome  feature.  The 
major  arguments  for  the  preference  of  the  rough  side  are:  It 
takes  the  ink  better,  can  be  penciled  on  also,  and  the  tendency  to 
curl  up  is  a  minimum.  With  a  little  practice  and  care,  erasures 
can  be  readily  and  neatly  made  on  this  side  of  the  cloth,  and 
for  general  purposes,  the  writer  advocates  the  use  of  the  rough 
surface. 

To  use  the  cloth,  stretch  it  taut,  smooth,  and  even  over  the 
drawing  to  be  traced  and  proceed  as  when  inking  on  paper. 
Should  the  ink  have  a  tendency  to  skip  or  be  ragged,  the  cause 
may  be  removed  by  rubbing  chalk  dust  over  the  surface  and 
then  polishing  it  off. 

121.  To  Make  an  Erasure  on  Tracing-cloth. — To  erase  ink 
from  tracing-cloth,  use  the  erasing-knife  as  described  for  eras- 


H4  MECHANICAL  DRAWING. 

ing  on  paper  until  the  line  is  quite  dim;  then  the  ink  eraser,, 
followed  by  the  pencil  eraser;  then  resurface  the  spot  erased  by 
rubbing  the  surface  with  soapstone  and  polish  with  a  cloth. 
The  tracing-cloth  can  then  be  again  inked  on  without  any  ten- 
dency to  blot. 

To  remove  pencil-lines  and  to  clean  tracing- cloth  apply  a 
rag  saturated  with  gasoline  or  benzine. 

No  water  should  be  allowed  to  get  on  the  cloth,  as  it  destroys 
the  surface  and  renders  it  unfit  for  use. 

Tracing-cloth  is  supplied  by  the  trade  in  the  form  of  rolls  of 
various  lengths  and  widths. 


CHAPTER  V. 

THE  REPRODUCTION  OF  DRAWINGS. 

122,  Introductory. — Mechanical  drawing  is  an  art  to  facilitate 
manufacture.  No  longer  is  the  construction  of  a  bit  of  mechanism, 
a  machine,  a  dwelling-house,  a  bridge,  etc.,  a  "cut  and  try" 
operation;  rather,  have  such  undertakings  become  "exact  sciences " 
because  of  drawing  and  design.  When  such  works  are  now  pro- 
posed, the  entire  scheme  is  worked  out  beforehand  to  the  smallest 
detail;  drawings  of  all  the  parts  or  works  are  made,  forming 
what  is  called  the  "plans"  for  the  undertaking,  which,  together 
with  any  necessary  additional  information,  called  the  "specifica- 
tions," forms  a  safe,  accurate,  and  complete  guide  for  the  work. 

Let  it  be  assumed  that  a  machine  is  to  be  produced;  the 
design  having  been  worked  out,  accurate  mechanical  draw- 
ings of  the  machine  as  a  whole,  and  of  its  component  parts,  are 
drawn  to  scale;  these  drawings  are  to  be  the  "guide"  for  the 
artisan  in  his  work;  that  is,  the  shopman  must  have  "something 
to  go  by."  Should  the  original  drawings  be  sent  into  the  shop  it 
is  quite  probable  that  they  would  soon  become  soiled  and  illegible 
in  the  grimy  hands  of  the  workman  and  the  design  lost.  The 
production  of  the  drawings  has  cost  the  manufacturer  a  con- 
siderable sum  of  money  and  he  can  ill  afford  to  have  original 
drawings  go  into  the  shop;  the  universal  practice  is  to  furnish 
a  duplicate  drawing  to  the  workmen  and  to  keep  the  original  on 
file  in  the  draughting-room. 

Besides  the  reason  cited  above,  the  manufacturer  must  pre- 
serve the  drawings  as  a  "receipt"  for  the  undertaking  in  case 
of  future  orders  for  the  same  design;  also,  the  drawings  may 
be  needed  at  different  points  at  the  same  time;  for  these  and 

"5 


n6  MECHANICAL   DRAWING. 

many  other  obvious  reasons  it  is  necessary  that  original  drawings 
be  duplicated  and  the  originals  preserved. 

An  exception  to  the  foregoing  is  the  occasional  practice  of 
mounting  original  drawings  on  cardboard,  sheet  iron,  wood,  etc., 
protecting  the  drawings  with  a  glass  cover,  a  coat  of  varnish, 
shellac,  etc.,  then  sending  them  into  the  shop.  Such  a  practice 
is  limited,  and  is  usually  employed'  where  the  work  is  stand- 
ard— tables  of  standards,  shop-cards,  etc. — and  the  drawings  are 
needed  permanently  in  one  place. 

Drawings  may  be  duplicated  in  various  ways,  principal 
among  which  are  by  blue-print  process,  by  photography,  by  the 
hectograph  and  similar  processes,  and  by  the  mimeograph,  being 
named  in  the  order  of  their  importance  for  practical  pui  poses. 

123.  Blue-printing. — Blue-printing  is  the  almost  universal 
method  of  reproducing  drawings  for  practical  purposes,  the  draw- 
ings being  made  on  tracing  linen.  By  this  method  an  unlimited 
number  of  duplicates  may  be  made,  the  most  serious  objection 
to  the  practice  being  that  good  sunlight  is  required  for  the  print- 
ing, an  erstwhile,  very  serious  objection  when  it  is  remembered 
that  during  the  winter  months  the  sun  does  not  shine  for  days 
at  a  time;  however,  this  objection  is  eliminated  by  the  present- 
day  practice  of  printing  by  electric  light,  and  minimized  to  quite 
a  degree  by  rapid- printing  paper  which  will  print  in  a  compara- 
tively short  time  on  the  darkest  of  days.  The  operation  is  a 
very  cheap  one,  and  a  good  blue- print  is  both  beautiful  and  clear 
to  the  eye;  it  does  not  show  dirt  and  is  admirably  adapted  for 
use  in  the  shop. 

To  duplicate  a  drawing  by  this  process  requires  the  use  of 
some  such  printing-frame  as  is  depicted  on  page  188,  the  pro- 
cedure being  as  follows:  With  the  back  of  the  printing- frame 
removed,  place  the  drawing  (tracing)  in  the  frame  with  the  inked 
side  next  to  the  glass;  next  place  the  prepared  paper  in  the  frame 
with  the  prepared  side  next  to  the  tracing,  close  the  frame  by 
putting  the  back  in  position,  and  see  that  it  is  well  secured  by 
the  springs  and  catches;  this  done,  carefully  inspect  the  drawing- 
and  print-paper  (through  the  glass  front)  and  see  that  they  have 


REPRODUCTION   OF  DRAWINGS.  117 

good  contact  with  each  other  and  with  the  glass  and  are  free  from 
folds  and  wrinkles;  when  the  arrangement  passes  inspection  expose 
the  frame  to  the  sun  in  a  position  as  nearly  at  right  angles  to  its 
rays  as  is  possible  and  for  a  length  of  time  suitable  to  the  paper, 
then  remove  the  paper  (not  the  tracing)  and  wash  it  (the  paper) 
for  three  or  four  minutes  in  a  bath  of  clear  water  and  then  hang  it 
up  to  dry. 

The  explanation  of  the  phenomenon  is,  the  paper  is  sensi- 
tized with  a  preparation  which  is  susceptible  to  the  sunlight,  and 
when  the  printing-frame  is  exposed,  all  parts  of  the  print-paper 
exposed  to  the  sun  are  affected  by  its  rays.  Not  so  with  those 
portions  of  the  paper  directly  beneath  the  lines  of  the  drawing; 
these  are  protected  from  the  sun  by  the  opaque  deposit  of  ink  on 
the  tracing  cloth  and  this  leaves  a  design  on  the  paper— the 
duplicate  of  the  tracing — unaffected  by  the  sunlight.  Should  the 
printing  proceed  beyond  the  proper  time  exposure,  the  sun's  rays 
will  gradually  pierce  the  lines  of  the  drawing  and  the  entire  sur- 
face of  the  paper  will  become  affected,  presenting  a  uniform  field 
and  no  "print";  also,  should  the  exposure  not  be  of  the  proper 
length  of  time,  the  paper  will  not  be  acted  on  by  the  sunlight 
long  enough  to  produce  sufficient  contrast  and  again  give  a  uniform 
field  and  no  "  print." 

From  the  above  it  is  evident  that  there  is  a  limited  exposure 
necessary  for  good  results;  also  that  it  is  then  necessary  to  in 
some  manner  "fix"  the  print,  rendering  it  immune  to  further 
exposures;  this  is  done  by  the  water-bath,  the  water  "fixing" 
the  exposed  surface  and  dissolving  the  preparation  from  the 
unexposed  design.  The  paper  used  for  the  production  of  the 
process  paper  is  originally  a  white  paper;  when  sensitized,  a 
dull- gray  or  greenish  color;  when  exposed,  a  deep  gray,  and 
when  washed,  a  shade  of  blue,  from  light  to  dark  according  to  the 
length  of  the  exposure.  The  protected  parts  remain  the  original 
dull-gray  or  greenish  color,  and  when  washed  present  the  white 
paper  beneath,  thus  giving  white  lines  on  a  blue  background, 
the  ordinary  blue-print. 

124.  Exposure. — If   an   exposure   results   in   an   entire   very 


n8  MECHANICAL  DRAWING. 

deep-blue  field,  the  exposure  has  been  too  long,  or  else  the  lines 
of  the  drawing  were  transparent,  the  ink  used  unfit  for  printing 
purposes;  if  the  result  be  a  light,  milky- looking  print,  the  exposure 
was  of  too  short  duration.  "The  newer  the  paper  the  longer  to 
print  and  quicker  to  wash;  the  older  the  paper  the  quicker  to 
print  and  longer  to  wash." 

125.  Washing. — The  washing  of  the  prints  is  a  very  par- 
ticular step  in  the  process,  as  a  too  long  washing  will  have  a 
tendency  to  wash  out  the  print,  ultimately  dissolving  all  of  the 
preparation  and  presenting  the  original  white  paper;    a  short 
bath  does  not  give  sufficient  time  for  the  water  to  completely 
dissolve  the  preparation  from  the  unexposed  parts  of  the  paper, 
and  when  again  exposed  to  light   (in  use)  the  print  will  soon 
succumb  to  the  sun's  rays  and  the  design  fade  away. 

Prints  may  be  kept  in  a  dark  place  for  quite  a  length  of  time 
before  being  washed,  though  it  is  preferable  to  wash  them  soon 
after  printing. 

126.  Drying. — For  drying  prints,  the  best  results  are  obtained 
by  " hanging  up";   a  good  arrangement  is  a  frame  containing  a 
number  of  "clip"  fasteners — spring  clothes  pins.    When  dry  the 
print  will  be  more  or  less  "curled  up";    to  straighten,  draw  it 
over   a   sharp  table- edge   two  or  three  times,  or  take   it   down 
while  yet  a  little  moist  and  place  it  in  a  press. 

A  print  when  once  made  is  a  permanent  "job"  and  any 
corrections  or  alterations  should  be  made  on  the  tracing  and  a 
new  print  made.  However,  if  the  desired  change  be  not  of  much 
import  and  not  requiring  much  labor,  the  print  may  be  marked  on 
with  a  solution  of  common  washing-soda  and  water. 

After  some  experience  one  is  able  to  judge  of  the  proper  expos- 
ure for  a  paper  by  the  change  in  color  of  the  preparation.  When- 
using  such  a  frame  as  shown  on  page  188,  the  paper  may  be  in- 
spected by  raising  one  part  of  the  two-part  back  and  noting  the 
change  in  color;  if  under-exposed,  the  frame  can  be  closed  again 
and  the  exposure  continued,  the  tracing  and  paper  having  been 
held  in  position  by  the  closed  half  of  the  back.  If  no  such  frame 
is  to  be  had,  a  test  piece  of  paper  may  be  placed  in  one  corner  of 


REPRODUCTION  OF  DRAWINGS.  119 

4 

the  frame  and  exposed  along  with  the  tracing,  and  when  this 
is  of  the  proper  color  the  paper  should  be  removed  and  washed. 

127.  Photography. — The  art  of  reproducing  by  photography 
is  a  branch  of  the  "trade"  of  photography.     Under  this  heading 
is  also   included   the   various  photogravure  processes   by  which 
plates   are   produced    for   press-printing.     This    is    the   method 
employed   by   the  publishers    of    text  books,    technical    papers, 
magazines,  etc.,  and  while  of  vast  importance  in  this  field,  it  has 
a  small  place  in  the  field  of  manufacture. 

128.  The  Hectograph. — The   hectograph  process  of  duplicat- 
ing drawings  is  a  process  much  used  by  architects  and  others 
when  but  a  limited  number  of  copies  are  required.     It  has  the 
advantage  of  producing   drawings   in   colors.     The   drawing   is 
made   on   smooth   paper  with   specially   prepared   aniline   inks, 
and  is  then  copied  on  the  hectograph — a  slab  coated  with  gela- 
tin— by  pressing  the  drawing  on  its  surface,  thus  transferring 
part  of  the  ink  from  the  drawing  to  the  gelatin  of  the  pad,  where 
it  is  retained  after  the  original  has  been  removed.    To  make  a 
copy,  blank  paper  is  pressed  on  the  surface  of  the  hectograph 
and  well  rubbed  so  that  the  contact  is  perfect,  when  the  gelatin, 
giving  up  part  of  the  ink  deposit,  gives  an  exact  copy  in  colors 
of  the  original  drawing.    The  copy  is  then  removed  from  the  pad 
and  when  dry  is  ready  for  use. 

129.  The   Mimeograph. — The  mimeograph  has  no  commer- 
cial rating  as  a  copying  process  for  mechanical  drawings  for 
shop  purposes,  but  is  valuable  as  a  means  for  duplicating  notes, 
small  and  fairly  simple  diagrams,   etc.    A  very  large  number 
of  copies  are  to  be  had  by  this  process.    The  drawing  or  copy 
is  made  on  a  specially  prepared  paper  by  moving  a  pointed  stylus, 
as  in  drawing  or  writing,  over  the  paper  when  on  a  finely  grooved 
steel  plate,  thus  tracing  the  copy  in  a  series  of  minute  perforations. 
The  stencil  is  then  suspended  in  a  special  frame,  and  by  means 
of  an  ink-roller,  ink  is  forced  through  the  perforations  onto  blank 
paper  placed  beneath  the  stencil,  producing  a  fac-simile  of  the 
stencil.     Stencils  may  also  be  made  on  a  typewriter. 


CHAPTER  VI. 
PATENT-OFFICE  DRAWINGS* 

130.  Introductory. — Draughtsmen   are  often   called   upon   to 
execute  drawings  for  presentation  to  the  United  States  Patent 
Office,  and  that  the  requisites  of  that  office  and  method  of  pro- 
cedure may  be  known,  the  following  remarks  are  taken  from  the 
"Rules  of  Practice  in  the  United  States  Patent  Office." 

131.  Drawings. — The  applicant  for  a  patent  is  required  by 
law  to  furnish  a  drawing  of  his  invention  whenever  the  nature  of 
the  case  admits  of  it. 

132.  Requisites   of   Drawings.— The.  drawing  may  be  signed 
by  the  inventor,  or  the  name  of  the  inventor  may  be  signed  on 
the  drawing  by  his  attorney  in  fact,  and  must  be  attested  by  two 
witnesses.     The  drawing  must  show  every  feature  of  the  inven- 
tion covered  by  the  claims,  and  the  figures  should  be  consecu- 
tively  numbered   if   possible.     When    the   invention   consists   of 
an  improvement  on  an  old  machine  the  drawing  must  exhibit, 
in  one  or  more  views,  the  invention  itself  disconnected  from  the 
old  structure,  and  also  in  another  view  so  much  only  of  the  old 
structure  as  will  suffice  to  show  the  connection  of  the  invention 
therewith. 

133.  Three  Editions  of  Drawings. — Three  several  editions  of 
patent  drawings  are  printed  and  published:    one  for  office  use, 
certified  copies,  etc.,  of  the  size  and  character  of  those  attached 
to  patents,  the  work  being  about  six  by  nine  and  one- half  inches; 
one  reduced  to  half  that  scale,  or  one-fourth  the  surface,  of  which 
four  are  printed  on  a  page  to  illustrate  the  volumes  distributed 
to  the  courts;    and  one  reduction — to  about  the  same  scale — • 
of  a  selected  portion  of  each  drawing  for  the  Official  Gazette. 

*  Extract  from  "Rules  of  Practice  in  the  United  States  Patent  Office." 

120 


PATENT  OFFICE  DRAWINGS.  1 21 

134.  Uniform   Standard.— This  work  is  done  by  the  photo- 
lithographic process,  and  therefore  the  character  of  each  original 
drawing  must  be  brought  as  nearly  as  possible  to  a  uniform 
standard  of  excellence,  suited  to  the  requirements  ot  the  process 
and  calculated  to  give  the  best  results,  in  the  interests  of  inventors, 
of  the  office,  and  of  the  public.     The  following  rules  will  there- 
fore be  rigidly  enforced,  and  any  departure  from  them  will  be 
certain  to  cause  delay  in  the  examination  of  an  application  for 
letters  patent: 

135.  Paper  and  Ink. — (i)  Drawings  must  be  made  upon  pure 
white  paper  of  a  thickness  corresponding  to  three- sheet  Bristol- 
board.     The  surface  of  the  paper  must  be  calendered  and  smooth. 
India  ink  alone  must  be  used,  to  secure  perfectly  black  and 
solid  lines. 

136.  Size  of  Sheet  and  Marginal  Lines. — (2)  The  size  of  a 
sheet  on  which  a  d/awing  is  made  must  be  exactly  ten  by  fifteen 
inches.     One  inch  from  its  edges  a  single  marginal  line  is  to  be 
drawn,  leaving  the  "sight"  precisely  eight  by  thirteen  inches. 
Within  this  margin  all  work  and  signatures  must  be  included. 
One  of  the  shorter  sides  of  the  sheet  is  regarded  as  its  top,  and 
measuring  downwardly  from  the  marginal   line  a  space  of  not 
less  than  one  and  one-quarter  inches  is  to  be  left  blank  for  the 
heading  of  title,  name,  number,  and  date. 

137.  Character  and  Color  of  Lines. — (3)  All  drawings  must 
be  made  with  the  pen  only.    Every  line  and  letter  (signatures 
included)  must  be  absolutely  black.    This  direction  applies  to  all 
lines,  however  fine,   to  s  ading,  and  to  lines  representing  cut 
surfaces  in  sectional  views.     All  lines  must  be  clean,  sharp,  and 
solid,  and  they  must  not  be  too  fine  or  crowded.     Surface  shad- 
ing, when  used,  should  be  open.     Sectional  shading  should  be 
made  by  oblique  parallel  lines,  which  may  be  about  one- twentieth 
of  an  inch  apart.     Solid  black  should  not  be  used  for  sectional 
or  surface  shading. 

138.  Few  Lines    and  Little  or  No  Shading. — (4)   Drawings 
should  be  made  with  the  fewest  possible  lines  consistent  with 
clearness.    By  the  observance  of  this  rule  the  effectiveness  of 


122  MECHANICAL   DRAWING. 

the  work  after  reduction  will  be  much  increased.  Shading 
(except  on  sectional  views)  should  be  used  only  on  convex  and 
concave  surfaces,  where  it  should  be  used  sparingly,  and  may 
even  there  be  dispensed  with  if  the  drawing  is  otherwise  well 
executed.  The  plane  upon  which  a  sectional  view  is  taken 
should  be  indicated  on  the  general  view  by  a  broken  or  dotted 
line.  Heavy  lines  on  the  shade  sides  of  objects  should  be  used, 
except  where  they  tend  to  thicken  the  work  and  obscure  letters 
of  reference.  The  light  is  always  supposed  to  come  from  the 
upper  left-hand  corner  at  an  angle  of  forty-five  degrees.  Imita- 
tions of  wood  or  surface  graining  should  not  be  attempted. 

139.  Scale  of  ttie  Drawing. — (5)  The  scale  to  which  a  draw- 
ing is  made  ought  to  be  large  enough  to  show  the  mechanism 
without  crowding,  and  two  or  more  sheets  should  be  used  if  one 
does  not  give  sufficient  room  to  accomplish  tnis  end;  but  the 
number  of  sheets  must  never  be  more  than  is  absolutely  neces- 
sary. 

140.  Letters  of  Reference. — (6)  The  different  views  should 
be  consecutively  numbered.  Letters  and  figures  of  reference 
must  be  carefully  formed.  They  should,  if  possible,  measure  at 
least  one-eighth  of  an  inch  in  height,  so  that  they  may  bear  re- 
duction to  one  twenty- fourth  of  an  inch;  they  may  be  much  larger 
when  there  is  sufficient  room.  They  must  be  so  placed  in  the  close 
and  complex  parts  of  drawings  as  not  to  interfere  with  a  thorough 
comprehension  of  the  same,  and  therefore  should  rarely  cross 
or  mingle  with  the  lines.  When  necessarily  grouped  around  a 
certain  part,  they  should  be  placed  at  a  little  distance,  where 
there  is  available  space,  and  connected  by  short  broken  lines 
with  the  parts  to  which  they  refer.  They  must  never  appear 
upon  shaded  surfaces,  and  when  it  is  difficult  to  avoid  this,  a 
blank  space  must  be  left  in  the  shading  where  the  letter  occurs, 
so  that  it  shall  appear  perfectly  distinct  and  separate  from  the 
work.  If  the  same  part  of  an  invention  appear  in  more  than 
one  view  of  the  drawing  it  must  always  be  represented  by  the 
same  character,  and  the  same  character  must  never  be  used  to 
designate  different  parts. 


PATENT-OFFICE  DRAWINGS. 


123 


PLATE  No.  10. 


U.S.   PATENT  OFFICE  CONVENTIONS 


Yellow  Red  Blue  Green  Purple  Black  Oran 


Motor-Generator  Storage  Cell 


Rheostat 


Transformer  Thermo-Elect-Gen.  Battery 


-lAAAAMAAAA— 

Resistance 


Triangular 


Tri-Phase  Connections 


Pole  Changer       Switch 

A  I 


Solenoid       Condenser ' 


Aft{\\Y\A^~^> 


Joinod  Wires 


Arc  Lamps 


Plus     Minus    Plus  or  Minus 


124  MECHANICAL   DRAWING. 

141.  Signatures  of  Inventor  and  Witnesses. — (7)  The  signa- 
ture of  the  inventor  should  be  placed  at  the  lower  right-hand 
corner  of  each  sheet,  and  the  signatures  of  the  witnesses  at  the 
lower  left-hand  corner,  all  within  the  marginal  line,  but  in  no 
instance  should  they  trespass  upon  the  drawings. 

142.  Title. — The  title 'should  be  written  with    pencil  on  the 
back  of  the   sheet.      The   permanent   names   and   title   will   be 
supplied  subsequently  by  the  office  in  uniform  style. 

143.  Large  Views. — When  views  are  longer  than  the  width 
of  the  sheet,  the  sheet  should  be  turned  on  its  side,  and  the  head- 
ing will  be  placed  at  the  right  and  the  signatures  at  the  left,  occupy- 
ing the  same  space  and  position  as  in  the  upright  views,  and  being 
horizontal  when  the  sheet  is  held  in  an  upright  position;    and 
all  views  on  the  same  sheet  must  stand  in  the  same  direction. 
One  figure  must  not  be  placed  upon  another  or  within  the  outline 
of  another. 

144.  Figure  for  Gazette. — (8)  As  a  rule,  one  view  only  of 
each  invention  can  be  shown  in  the  Gazette  illustrations.    The 
selection  of  that  portion  of  a  drawing  best  calculated  to  explain 
the  nature  of  the  specific  improvement  would  be  facilitated  and 
the  final  result  improved  by  the  judicious   execution   of  a  figure 
with  express  reference  to  the  Gazette,  but  which  might  at  the 
same  time  serve  as  one  of  the  figures  referred  to  in  the  specifica- 
tion.    For  this  purpose  the  figure  may  be  a  plan,  elevation,  sec- 
tion,   or  perspective   view,   according   to   the  judgment  of   the 
draughtsman.     It  must  not  cover  a  space  exceeding  16  sq.  ins. 
All  its  parts  should  be  especially  open  and  distinct,  with  very 
little  or  no  shading,  and  it  must  illustrate  the  invention  claimed 
only,  to  the   exclusion   of  all  other  details.     When  well  executedr 
it  will  be  used  without  curtailment  or  change,  but  any  excessive 
fineness,  or  crowding,  or  unnecessary  elaborateness  of  detail  will 
necessitate  its  exclusion  from  the  Gazette. 

145.  Drawings  to  be  Rolled  for  Transmission. — (9)  Drawings 
should  be  rolled  for  transmission  to  the  office,  not  folded. 

146.  No  Stamp,  Advertisement,  or  Address  Permitted  on  the 
Face  of  Drawings. — An  agent's  or  attorney's  stamp  or  advertise- 


PATENT-OFFICE  DRAWINGS.  125 

ment  or  written  address  will  not  be  permitted  upon  the  face  of  a 
drawing,  within  or  without  the  marginal  line. 

147.  Drawings  for  Designs. — In  certain  cases  these  rules  may 
be  modified  as  to  drawings  for  designs. 

148.  Drawings  for  Reissue  Applications. — All  reissue  appli- 
cations must  be  accompanied  by  new  drawings  of  the  character 
required  in  original  applications,  and  the  inventor's  name  must 
appear  upon  the  same  in  all  cases;   and  such  drawings  shall  be 
made  upon  the  same  scale  as  the  original  drawing,  or  upon  a 
larger  scale,  unless  a  reduction  of  scale  shall  be  authorized  by 
the  Commissioner. 

149.  Defective  Drawings. — The   foregoing   rules   relating   to 
drawings  will  be   rigidly   enforced.     Every   drawing  not   artis- 
tically executed  in  conformity  thereto  may  be  admitted  for  pur- 
poses of  examination  if  it  sufficiently  illustrates  the  invention, 
but  in  such  cases  a  new  drawing  must  be  furnished  before  the 
application  can  be  allowed.     The  office  will  make  the  necessary 
corrections  at  the  applicant's  option  and  cost. 

150.  Drawings  Furnished  by  Office. — Applicants  are  advised 
to  employ  competent  artists  to  make  their  drawings. 

The  office  will  furnish  the  drawings  at  cost,  as  promptly  as 
its  draughtsman  can  make  them,  for  applicants  who  cannot 
otherwise  conveniently  procure  them. 


CHAPTER  VII. 

GEARING. 

151.  Introductory. — A  gear-wheel  is  a  wheel  with  teeth  spaced 
around   its  circumference,   and  is  used  to   transmit  motion  by 
rolling   contact   with   other   toothed   wheels.      Gear-wheels   are 
much  used  in  the  construction  of  machinery,  the  planning  for 
which  means  that  they,  like  other  details,  must   be  worked  out 
and  pictured  by  the  draughtsman- designer. 

The  subject  "Gear- wheels  and  Gearing"  is  one  of  much 
magnitude,  there  being  several  systems  of  forms  of  gear-teeth, 
many  kinds  of  gear-wheels,  and  an  endless  arrangement  of  the 
various  wheels.  It  forms  a  part  of  the  study  of  " Mechanism"; 
however,  as  the  draughtsman  often  has  occasion  to  draw  gear- 
wheels without  any  reference  whatever  to  the  " design,"  the 
study  of  the  usual  forms  of  teeth  is  properly  a  part  of  this  work. 
It  is  the  purpose  of  these  remarks  to  treat  the  subject  from  the 
draughtsman's  standpoint,  and,  eliminating  as  much  of  the 
theory  as  is  possible,  to  acquaint  the  student  with  the  several 
forms  of  teeth  and  kinds  of  gears,  and  to  instruct  him  how  to 
draw  them. 

152.  Fundamental    Curves. — As    a   preliminary,    the   student 
must  acquaint  himself  with  the  elementary  curves  used  to  form 
the  tooth  curve   and  the  manner  of  their  construction.     These 
curves,  for  the  usual  forms  of  teeth,  are  four  in  number,  and  are 
(i)  the  cycloid,  (2)  the  epicycloid,  (3)  the  hypocycloid,  and  (4) 
the  involute. 

The  Cycloid. — Fig.  57.  If  a  circle  be  rolled  along  a  straight 
line,  every  point  in  its  circumference  will  describe  a  curve  known 
as  the  cycloid.  For  example,  assume  a  buggy- wheel  rolling 

126 


GEARING. 


127 


along  a  level  road,  the  travel  of  any  particular  point  on  the  rim 
is  a  cycloid. 

To  construct  the  curve,  draw  the  indefinite  straight  line  A-B 
as  a  base  line,  then  draw  the  circle  at  the  left  of  the  diagram  and 
divide  its  circumference  into  a  number  of  equal  arcs — twelve 


K'        J'        I'        H' 

FIG.  57. 


being  a  good  working  number,  though  the  greater  the  number 
the  more  nearly  accurate  the  work  becomes — as  O-D,  D-E,  etc. 
Next  lay  off  the  lengths  O-N',  N'-M',  etc.,  equal  to  the  length 
of  the  arc  O-D  and  erect  the  perpendiculars  O-C,  N'-C»  etc. 
[It  will  be  noted  that  the  circle  is  divided  into  an  equal  number 
of  equal  arcs;  this  facilitates  the  construction,  as  the  lengths  dealt 
with  are  uniform,  and  the  curve*  may  be  laid  out  symmetrically 
with  a  center  line  (7'-O6).  However,  the  circle  may  be  divided 
in  any  manner,  provided  the  various  lengths  be  used  properly.] 
Lastly,  draw  the  lines  /-/,  J-H,  etc.,  parallel  to  the  base  line 
A-B.  Now  assume  the  circle  to  roll  to  the  right;  when  the 
point  N  has  reached  N',  the  center  of  the  circle,  C,  has  traveled 
to  Ct;  with  this  point  as  a  center  and  the  proper  radius — that  of 
the  rolling  circle — by  describing  an  arc  intersecting  the  line  N-D, 
the  point  O  is  found  to  be  at  O—  the  point  O  is  the  point  taken 
for  the  example.  By  proceeding  in  this  manner  until  the  circle 
has  traversed  its  circumference,  and  using  the  successive  posi- 
tions of  the  center-point,  C,  a  series  of  points,  O,  Olt  O2,  O3,  etc., 
are  obtained  through  which  the  cycloid  is  drawn. 

The  Epicycloid. — Fig.  58.  If  a  circle  be  rolled  around  the 
outside  of  a  fixed  circle,  every  point  in  the  circumference  of  the 
rolling  circle  will  describe  a  curve  known  as  the  epicycloid. 

To  construct  the  curve,  draw  the  fixed  circle  A-B,  then  draw 


128 


MECHANICAL   DRAWING. 


the  rolling  circle  O-D-E,  etc.  (the  circle  at  the  extreme  left  of 
the  diagram),  and  divide  its  circumference  into  an  equal  number 
of  equal  arcs,  as  O-D,  D-E,  etc.;  next  lay  off  the  arcs  O-Nf,  N'-Mf, 
etc.,  on  the  circumference  of  fixed  circle  A-B,  equal  to  the  arc 
O-D  of  the  rolling  circle,  and  draw  the  radial  lines  through 
these  points;  lastly,  draw  the  circular  arcs  through  the  points 
of  division  on  the  circumference  of  the  rolling  circle  and 
through  its  center.  Now  assume  the  circle  to  roll  to  the 
right;  when  the  point  N  has  reached  N',  the  center  of  the 
circle  is  at  CL,  and  with  this  point  as  a  center  and  with  the 


FIG.  58. 


proper  radius — that  of  the  rolling  circle — by  describing  an  arc 
intersecting  the  circular  arc  N-D,  the  point  O  is  found  to  be  at. 
Or  By  thus  rolling  the  circle  to  the  right  for  a  complete  revo- 
lution, locating  the  successive  positions  of  the  center-point, 
Cly  C2,  C3,  etc.,  and  describing  the  proper  arcs,  a  series  of 
points,  O,  Oj,  O2,  etc.,  are  obtained  through  which  the  epi- 
cycloid is  drawn. 

The  Hypocycloid. — If  a  circle  be  rolled  around  the  inside 
of  a  fixed  circle,  every  point  in  the  circumference  of  the  rolling: 
circle  will  describe  a  curve  known  as  the  hypocycloid. 


GEARING. 


129 


The  manner  of  constructing  the  curve  is  identical  with  that 
given  for  the  epicycloid,  as  is  clearly  evident  from  Fig.  58. 

The  Involute. — Fig.  59.  If  a  straight  line,  or  to  be  consistent, 
a  circle  of  infinite  radius  be  rolled  around  the  outside  of  a  fixed 
circle,  every  point  in  it  will  describe  a  curve  known  as  the  involute. 
A  common  illustration  is  to  wind  a  string  about  a  cylinder,  then 
keeping  the  string  taut,  unwind  it;  the  end  of  the  string  will 
describe  an  involute. 


FIG.  59. 


To  construct  the  curve,  draw  the  circle  1-2-3,  etc.,  and  divide 
its  circumference  as  shown;  at  each  of  these  points  of  division 
draw  a  tangent  to  the  circle,  then  lay  off  the  lengths  2-1'  equal 
to  the  arc  2-1,  3-1'  equal  to  the  arc  3-1,  etc.;  that  is,  beginning 
at  a  certain  point,  the  length  of  the  tangent  at  any  point  must 
be  equal  to  the  length  of  the  rectified  arc  between  that  point 
and  the  starting-point. 

153.  Glossary  of  Terms. — The  projections  around  the  periph- 
ery of  a  gear-wheel  are  called  the  teeth  of  the  gear;  the  blank 
spaces  between  the  teeth  are  called  the  spaces.  The  width  of  a 
tooth  plus  the  width  of  a  space,  measured  on  a  certain  circle 
called  the  pitch- circle,  is  called  the  circular  pitch  of  the  gear. 


130  MECHANICAL  DRAWING. 

The  engaging  surface  of  a  tooth  projecting  beyond  the  pitch- 
circle  is  called  the  face  of  the  tooth;  the  engaging  surface  within  the 
pitch-circle  is  called  the  flank  of  the  tooth.  That  face  of  a  tooth 
first  coming  into  contact  is  called  the  front  of  the  tooth;  that 
face  coming  into  contact  later  is  called  the  back  of  the  tooth; 
thus  we  have  the  front  and  back  face  of  a  tooth,  and  the  front 
and  back  flank  of  a  tooth.  The  point  where  the  pitch- circle 
cuts  the  front  of  a  tooth  is  called  the  pitch-point  of  the  tooth. 
The  outer  end  of  a  tooth  is  called  the  addendum  end,  and  a 
circle,  concentric  with  the  gear,  drawn  through  it  is  called  the 
addendum-circle;  the  inner  "end"  of  a  tooth  is  called  the  root 
of  the  tooth,  and  a  circle,  concentric  with  the  gear,  drawn  through 
it  is  called  the  root- circle.  The  space  between  the  addendum- 
circle  of  one  gear  and  the  root-circle  of  the  gear  with  which  it 
engages  is  called  the  clearance  of  the  gears;  a  circle  denning  the 
clearance  of  a  gear  is  called  the  addendum- circle.  The  depth  of 
a  tooth  is  the  distance,  measured  radially,  between  the  addendum- 
and  root-circles  of  the  gear.  The  fillet  is  the  rounded  part  of 
the  flank,  fashioned  so  as  to  give  the  tooth  strength.  The  pitch- 
diameter,  or  simply  diameter  of  a  gear,  is  the  diameter  of  its  pitch- 
circle;  the  diametral  pitch  of  a  gear  is  the  ratio  of  the  number  of 
teeth  to  the  pitch-diameter.  The  gear  to  which  the  power  is 
applied  is  called  the  driver;  the  one  with  which  it  engages  is 
called  the  follower. 

-  Gears  are  designated  in  two  general  ways:  (i)  by  giving  the 
pitch-diameter  of  the  gear  and  number  of  teeth,  as  a  10"  gear 
having  40  teeth;  (2)  by  the  pitch-diameter  and  diametral  pitch 
of  the  gear,  as  (for  the  same  gear)  a  10"  four-pitch  gear. 

154.  Usual  Proportions  for  Teeth. — The  dimensions  of  the 
teeth  of  a  gear  are  determined  in  two  ways:  (i)  by  making  them 
proportional  to  the  circular  pitch,  and  (2)  by  proportioning  them 
to  the  diametral  pitch.  Both  methods  are  much  used;  also,  there 
are  several  proportions  in  use.  For  the  draughtsman  a  good 
method  is  to  draw  the  addendum  .3  of  the  circular  pitch,  meas- 
ured radially  out  from  the  pitch-circle;  the  dedendum  .3  of  the 

circular  pitch,  measured  in  a  like  manner  in  from  the  pitch-circle ; 


GEARING.  131 

the  clearance  to  be  .1  of  the  circular  pitch;    the  width  of  tooth 
and  space  to  be  equal  and  equal  to  one-half  of  the  circular  pitch. 
155.  Development  of  Formulae. 
Let  D  =  the  diameter  of  the  gear. 

C  =  the  circumference  of  the  gear  =  3.  1416X^  =  7:^. 
.2V  =  the  number  of  teeth. 

Q 

P  =  the  circular  pitch  =  -^  .........     (i) 

AT 
P'  =  the  diametral  pitch  =  —  .........     (2) 

Then,  with  the  diameter  and  circular  pitch  given,  to  find  the 
number  of  teeth, 


(3) 


With  the  diameter  and  diametral  pitch  given,   to  find  the 
number  of  teeth, 

N-P'D (4) 

Placing  the  two  values  of  N  equal  to  each  other, 
Substituting  nD  for  C, 


Hence 

r-  .........  (s) 


(6) 
(7) 


156.  Kinds  of  Gears.  —  Of  the  several  kinds  of  gears  met 
with  in  practice,  three  have  been  chosen  and  will  be  discussed 
as  being  representative  of  those  most  frequently  confronting 


132  MECHANICAL  DRAWING. 

the  draughtsman,  i.  A  spur- gear  is  a  gear  whose  teeth  are  on 
the  outside  of  the  gear.  2.  A  rack  is  a  spur-gear  whose  radius 
is  infinity;  here  the  pitch-circle  becomes  a  pitch-line,  the  adden- 
dum-circle the  addendum- line,  etc.  3.  An  annular  or  internal 
gear  is  a  gear  whose  teeth  are  on  the  inside  of  the  gear. 

157.  Systems  of  Teeth. — Like  the  kinds  of  gears,  there  are 
several  systems  of  tooth  outline;    of  these  but  two  are  widely  in 
use:  (i)  the  cycloidal  system,  and  (2)  the  involute  system. 

The  form  of  the  tooth  curve  adopted  for  the  rack  is  the  deter- 
mining basis  for  the  systems.  If  the  tooth  curve  is  composed 
of  cycloidal  curves,  the  resulting  system  is  called  the  cycloidal 
system;  when  the  tooth  curve  be  omes  a  straight  line  the  resulting 
system  is  called  the  involute  system. 

In  the  cycloidal  system  the  tooth  curve  is  described  by  certain 
circles,  called  describing-circles,  rolling  on  the  pitch- circle  of 
the  gear;  in  the  involute  system  the  tooth  curve  is  formed  by  the 
involute  to  a  certain  circle,  called  the  base-circle,  drawn  tangent  to 
a  certain  straight  line,  called  the  line  oj  action,  drawn  through 
the  common  pitch- point  of  the  two  gears,  and  a  radial  line  drawn 
from  the  origin  of  the  involute. 

158.  Interchangeability. — Gears   are   largely   made   to   work 
in  sets;   for  this  reason  it  is  necessary  that  the  teeth  be  so  fash- 
ioned that  the  gear  will  be  interchangeable  within  certain  limits. 

In  the  cycloidal  system,  if  the  gear  is  not  to-be  one  of  a  set,  a 
good  general  rule  is  to  make  the  diameter  of  the  rolling  circle 
equal  to  three-eighths  of  the  diameter  of  the  pitch- circle  in  which 
it  rolls;  if  the  gear  is  to  be  one  of  a  set,  a  universal  rule  is  to  make 
the  rolling  circles  for  the  set  of  a  uniform  diameter,  this  diameter 
to  be  equal  to  the  radius  of  a  gear  with  twelve  teeth  of  the  circular 
pitch  of  the  set,  the  fundamental  for  all  interchangeability  being 
a  uniform  circular  pitch. 

In  the  involute  system  the  gears  must  have  a  common  line  of 
action  and  a  uniform  circular  pitch. 

159.  Methods    of  Drawing    the   Tooth   Outline. — There  are 
several  practical  methods  for  drawing  the  tooth  curve;   to  treat  of 
all  of  them  is  beyond  the  scope  of  this  work,  and  the  discussion 


GEARING. 


'33 


will  be  limited  to  the  two  methods  most  widely  in  use.  i.  The 
"exact  method"  is  the  term  applied  to  the  procedure  when  the 
true  theoretical  tooth  curve  is  drawn.  2.  The  "approximate 
method"  is  the  term  applied  when  the  true  tooth  curve  is  approxi- 
mated. 

1 60.  Spur-gears.     Exact,    Non-interchangeable    Cycloidal. — 
Let  it  be  assumed  that  the  draughtsman  is  required  to  furnish 


the  pattern-maker  with  a  templet  for  laying  out  the  exact  tooth 
outline  for  certain  gears,  and  let  Fig.  60  represent  the  conditions. 
This  pair  of  gears  is  not  part  of  a  set,  simply  designed  to  work 


134  MECHANICAL  DRAWING. 

together;   note  also  that  the  gears  are  spur- gears  and  that  the 
teeth  are  of  the  cycloidal  system. 

To  draw  the  teeth,  draw  the  line  of  centers,  A-B,  properly 
locate  the  centers  and  draw  the  pitch-circles  E-E  and  E'-E'\ 
draw  the  describing- circles  as  shown,  and  of  a  diameter  equal 
to  three-eighths  of  the  diameter  of  the-  respective  pitch- circles. 
Now  roll  the  describing- circle  of  the  driver  to  the  right  and  inside 
of  the  E'-Ef  pitch-circle  and  describe  the  hypocycloid  i-h-i-j-k 
(Sect.  152);  this  curve  forms  the  flank  of  the  teeth  for  the  driver. 
Again  roll  the  same  describing- circle  to  the  right  and  this  time 
on  the  outside  of  the  E-E  pitch-circle  and  describe  the  epicycloid 
i-l-m-n  (Sect.  152);  this  curve  forms  the  face  of  the  teeth  for 
the  follower.  Next  roll  the  describing-circle  of  the  follower  to 
the  left  and  inside  of  the  E-E  pitch- circle  and  describe  the  hypo- 
cycloid  i-a-b-c-d; — this  curve  forms  the  flank  of  the  teeth  for  the 
follower.  Rolling  the  same  describing- circle  to  the  left  again, 
and  this  time  on  the  outside  of  the  E'-Ef  pitch-circle,  obtain 
the  epicycloid  i-e-f-g,  which  curve  forms  the  face  of  the  teeth  for 
the  driver.  The  tooth  curves  drawn,  draw  the  addendum, 
dedendum,  and  root- circles  for  the  gears  according  to  the  usual 
proportions  (Sect.  154),  the  circular  pitch  having  been  com- 
puted by  formula  i,  Sect.  155.  Starting  at  the  common  pitch- 
point,  i ,  step  off  one-half  of  the  circular  pitch  around  the  pitch- 
circles,  and  with  a  templet  of  the  proper  curve — an  irregular 
curve  properly  marked — through  these  points  draw  in  the  outlines 
of  the  teeth  as  shown. 

Exact,  Interchangeable  Cycloidal. — Assume  that  the  fol- 
lower of  the  above  example  is  to  form  part  of  a  set  of  gears,  and 
let  it  be  required  to  draw  the  exact  tooth  outline.  As  previously 
explained  (Sect.  158),  the  diameter  of  the  describing-circle  is 
predetermined — found  by  substituting  the  known  values  in 
formula  i  and  solving  for  D\  the  diameter  of  the  rolling  circle 
equals  one- half  of  D.  Let  Fig.  61,  showing  the  follower  in  gear 
with  the  smallest  gear  of  the  set,  represent  the  conditions. 

The  describing- circles  drawn,  the  method  of  procedure  is  iden- 
tical with  that  given  for  the  non- interchangeable  gear;    it  will 


GEARING. 


'35 


be  noted,  however,  that  the  hypocycloid  obtained  by  rolling 
the  describing-circle  inside  the  pitch-circle  of  the  driver  is  a 
straight  line  passing  through  the  center  of  the  pitch-circle,  making 
the  flanks  of  the  teeth  of  that  gear  to  be  radial  lines. 


Exact  Involute. — Let  it  be  required  to  draw  the  above  gears 
with  exact  involute  teeth,  and  let  Fig.  62  be  the  diagram.  To 
draw  the  teeth,  draw  the  two  pitch-circles  as  before,  then  draw 
the  line  of  action,  X-Y,  as  shown,  and  the  base  circles,  m-n  and 
p-py  tangent  to  it.  Next  draw  the  involutes  0-1-2-3,  etc->  an(* 
o'-2-3',  etc.,  to  the  m-n  and  p-p  base  circles,  respectively;  these 
curves  form  the  face  and  part  of  the  flank — that  part  between 
the  pitch- circle  and  the  base  circle — of  the  teeth  of  the  respective 
gears,  the  remainder  of  the  flanks  being  drawn  as  radial  lines. 


I36  MECHANICAL   DRAWING. 

With  the  depth  of  the  tooth  defined,  and  the  width  of  the  tooth 
and  space  laid  out  on  the  pitch- circles,  the  tooth  outline  is  drawn 
in  as  shown  by  means  of  templets  to  the  involutes. 


FIG.  62. 

The  construction  of  the  exact  tooth  curve  is  both  laborious 
and  time-consuming;  in  fact  so  much  so  that  there  has  been 
a  number  of  methods  evolved  for  approximating  the  curve.  Of 
the  various  methods  in  use,  that  of  approximating  the  tooth 
curve  with  circular  arcs  is  the  most  widely  used.  The  methods 
known  as  "Grant's  Epicycloidal  and  Involute  Odontographs" 
(see  tables),  the  invention  of  George  B.  Grant,  are  taken,  by 
permission  of  the  author,  from  "Grant's  Treatise  on  Gearing." 
They  have  nearly  supplanted  previous  devices  for  the  purpose 
in  this  country. 

The  use  of  the  tables  is  explained  by  the  following  examples : 
Approximate  Cycloidal.— Fig.  i,  Plate  No.  n.  Draw  the 
pitch-,  addendum-,  dedendum-,  and  root- circles  of  the  gears  and 
lay  off  the  width  of  tooth  and  space,  as  previously  explained. 
With  either  the  diametral  or  circular  pitch,  and  the  number  of 
teeth  known,  to  apply  the  table  look  in  the  column  of  teeth  for 


GEARING. 


137 


GRANT'S   TABLES   FOR   DRAWING    GEAR-TEETH.* 

(Standard  Interchangeable  Series.) 

GRANT'S  INVOLUTE  ODONTOGRAPH. 

Centers  on  Base  Line. 


Divide  by  the 
Diametral  Pitch. 

Multiply  by  the 
Circular  Pitch. 

Trrth 

icctn.      , 
Face 

Flank 

Face 

Flank 

Rad's. 

Rad's. 

Rad's. 

Rad's. 

10              2.28 

.69 

•73 

.22 

II                    2  .  40 

•83 

.76 

.27 

12 

2-51 

.96 

.80 

•31 

13 

2.62 

.09 

•83 

•34 

14 

2.72 

.22 

.87 

•39 

15 

2.82 

•34 

.90 

•43 

16 

2.92 

.46 

•93 

•47 

17 

3.02 

.58 

.96 

•50 

18 

3-12 

.69 

•99 

•54 

19 

3.22 

•79 

•03 

•57 

20 

3-32 

.89 

.06 

.60 

21 

3-4i 

.98 

.09 

.63 

22 

3-49 

2.06 

.11 

.66 

23 

3-57 

2.15 

•13 

.69 

24 

3-64 

2.24 

.16 

•71 

25 

2-33 

.18 

•74 

26 

3*78 

2.42 

.20 

•77 

27 

3-85 

2.50 

•23 

.80 

28 

3-92 

2-59 

•25 

.82 

29 

3-99 

2.67 

•27 

•85 

3° 

4.06 

2.76 

.29 

.88 

31 

4.I3 

2-85 

•31 

.91 

32 

4.20 

2-93 

•34 

•93 

33 

4.27 

3.01 

•36 

.96 

34 

4-33 

3-09 

•38 

.99- 

35 

4-39 

3.  16 

•39 

1.  01 

36 

4-45 

3-23 

.41 

1.03 

1  n  tc  rvti  i 

37-40 

4.20 

1-34 

41-45 

4-63 

1.48 

46-51 

5-o6 

1.61 

52-60 

5-74 

1.83 

61-70 

6.52 

2.07 

71-^0 

7.72 

2.46 

91-120 

9.78 

3.  ii 

121-180 

I3-38 

4.26 

181-360 

21.62 

6.88 

*  Taken,  by  permissu  n,  from  "Grant's  Treatise  on  Gearing." 


MECHANICAL   DRAWING. 
GRANT'S  CYCLOIDAL  ODONTOGRAPH. 


For  One  Diametral  Pitch. 

For  One  Inch  Circular  Pitch. 

Number  of  Teeth 

For  any  other  Pitch,  Divide 
by  that  Pitch. 

For  any  other  Pitch,  Multiply 
by  that  Pitch. 

Faces. 

Flanks. 

Faces. 

Flanks. 

Exact. 

Intervals. 

Rad's. 

Dist. 

Rad's. 

Dist. 

Rad's. 

Dist. 

Rad's. 

Dist. 

10 

IO 

1.99 

.02 

-    8.00 

4.00 

.62 

.OI 

-2-55 

1.27 

II 

12 

ii 

12 

2.OO 
2.OI 

.04 
.06 

—  1  1  .  05 
Infinity 

6.50 
Infinity 

•63 

.64 

.01 
.02 

-3-34 
Infinity 

2.07 
Infinity 

13^ 

13—14 

2.O4 

.07 

14.50 

9-43 

•65 

.02 

4.60 

3.00 

'5* 

15-16 

2.  IO 

.09 

7.86 

.67 

•03 

2.50 

I.  IO 

J7i 

17-18 

2.14 

.  II 

6-13 

2.  2O 

.68 

.04 

i-95 

.70 

20 

19-21 

2.20 

•13 

5.12 

i-57 

.70 

.04 

1.63 

•5° 

23 

22-24 

2.26 

•15 

4-5° 

i  .  13 

.72 

•°5 

1-43 

•36 

27 

25-29 

2-33 

.16 

4.10 

.96 

•74 

•°5 

1.30 

.29 

33 

30-36 

2.4O 

.19 

3.80 

.72 

.76 

.06 

1.20 

•23 

42 

37-48 

2.48 

.22 

3-52 

•63 

•79 

.07 

I.  12 

.20 

58 

49-72 

2.60 

.25 

3-33 

•54 

•83 

.08 

I.  06 

•17 

97 

73—144 

2.83 

.28 

3-  J4 

•44 

.90 

.09 

I.OO 

.14 

290 
Infinity 

145-300 

Rack 

2.92 
2.96 

•31 
•34 

3.00 
2.96 

•38 
•34 

•93 
•94 

.  IO 

.  ii 

•95 
•94 

.  12 
.11 

the  number  corresponding  to  the  number  of  teeth  of  the  gear  to 
be  drawn;  this  found,  follow  across  to  the  column  headed  "Face, 
Dist."  (diametral  or  circular  pitch,  as  the  case  may  be),  and 
applying  the  instructions  (to  divide  or  to  multiply)  given  in  the 
table,  lay  off  the  length  obtained  as  shown,  and  draw  the  circle 
of  face  centers.  Going  back  to  the  column  of  teeth  number  in 
the  table,  find  the  corresponding  " Rad's"  number,  and  in  accord- 
ance with  the  table  instruction,  compute  the  face  radius;  this 
found,  with  centers  on  the  face  radius  circle,  draw  the  face  curve 
of  the  teeth.  The  circle  of  flank  centers  and  flank  radii  are 
computed  from  the  table  in  a  similar  manner  and  the  flank 
curve  of  the  teeth  drawn  as  shown. 

Approximate  Involute. — Fig.  2,  Plate  No.  n.  The  table  for 
involute  teeth  is  applied  similarly  to  that  for  cycloidal  teeth,  with 
the  exception  that  all  centers  are  on  the  base  circle. 

161.  Rack  and  Pinion.  Exact,  Non-interchangeable  Cy- 
cloidal.— Fig.  63.  This  is  identical  with  the  same  conditions  given 
for  spur-gearing  (Sect.  160),  the  rack  being  a  spur-gear  of  in- 


GE/4RING. 


'39 


PLATE  No.  IT. 


GEARING 
DIFFERENT  SYSTEMS. 

Approximate  method. 


1.  CYCLOIDAL  SYSTEM. 

(By  Grant's  Cycloidal  Odontograph.) 

EXAMPLES  OF  SPUR  GEARS. 

J 


c' 


/ 

2.  INVOLUTE  SYSTEM. 

(By  Grant's  Involute  Odontograph.) 


140 


MECHANICAL  DRAWING. 


finite  radius  and  its  describing-circle  a  straight  line  E-E.      By 
rolling   the  describing-circle  of  the  pinion  on  the  inside  of  the 

iA 


FIG.  64. 

pitch-circle,   the  hypocycloid   P-M,   forming   the  flanks  of  the 
pinion  teeth,  is  obtained;    by  rolling  the  same  circle  along  the 


GEARING. 


141 


pitch-line,  the  cycloid  forming  the  faces  of  the  rack  teeth  is  ob- 
tained; by  rolling  the  line  E-E  around  the  pitch-circle  the  involute 
forming  the  faces  of  the  pinion  teeth  is  described;  the  flanks  of 
the  rack  teeth  are  drawn  perpendicular  to  the  pitch- line. 

Exact,  Interchangeable  Cycloidal. — Fig.  64  illustrates  the  ap- 


plication of  the  uniform  rolling  circle  of  a  set  of  gears,  and  the 
procedure  is  identical  with  that  given  in  Sect.  160. 

Exact  Involute. — Fig.  65.    Here  the  tooth  curve  of  the  rack 


FIG.  66. 

is  a  straight  line;  the  base  circle  and  involute  P-M  for  the  face 
of  the  teeth  of  the  pinion  are  obtained  in  the  usual  manner  and 
the  teeth  drawn  as  in  Sect.  160. 

Approximate  Cycloidal. — Fig.  66.    Apply  the  cycloidal  table 


142 


MECHANICAL  DRAWING. 


as  for  spur-gears,  the  face  and  flank  center  circles  for  the  rack 
becoming  straight  lines  parallel  with  the  pitch- lines. 

Approximate  Involute. — Fig.  67.     Draw  straight  lines  for  the 


FIG.  67. 

tooth  curve  of  the  rack  teeth,  and  for  the  tooth  curve  of  the  pinion 
apply  the  involute  table  as  for  spur-gears,  Sect.  160. 

A 


162.  Internal  Gears.  Exact  Cycloidal.— Fig.  68.  To  draw 
the  teeth,  draw  the  two  pitch- circles  tangent  at  the  common  pitch- 
point,  P;  draw  the  addendum-  and  root-circles  of  the  usual  pro- 


GEARING. 


143 


portions,  and  the  describing-circles  as  shown.  Rolling  the 
describing-circle  on  the  outside  of  the  large  pitch-circle  generates 
the  epicycloid  P-E,  which  defines  the  flank  curve  for  the  teeth 


for  the  annular  wheel;  rolling  the  same  describing-circle  on  the 
outside  of  the  pitch-circle  of  the  pinion  generates  the  epicycloid 
P-F,  which  defines  the  face  curve  for  the  teeth  for  the  pinion. 


FiQ.TO. 


Rolling  the  describing-circle  on  the  inside  of  the  pitch-circles  gen- 
erates the  hypocycloids  P-G  and  P-H,  which  form  the  face  curve 
of  the  teeth  for  the  wheel  and  the  flank  curve  for  the  teeth  of  the 


144 


MECHANICAL   DRAWING. 


pinion,  respectively.  The  tooth  curves  denned,  the  teeth  are 
drawn  by  means  of  a  templet. 

Exact  Involute. — Fig.  69.  Draw  the  two  pitch- circles  and 
the  line  of  action  as  shown;  draw  the  addendum- circle  of  the 
pinion  and  the  root-circle  of  the  wheel  as  usual.  The  addendum- 
circle  of  the  wheel  is  determined  by  the  point  F,  and  the  root- 
circle  of  the  pinion  by  the  usual  clearness.  To  draw  the  teeth, 
the  base  circles  are  drawn  as  for  spur- gears,  the  involutes  to 
them,  P-E'  and  P-F',  described,  and  the  teeth  drawn  as  shown. 

Approximate  Cycloidal. — Fig.  70.  The  pitch-,  addendum-,  and 
root-circles  are  drawn  in  the  usual  way  and  the  cycloidal  table 
applied  as  for  spur-gears. 

Approximate     Involute. — Fig.     71.     The    pitch-circles,    the 


O      PNQ 


ON  P     O 


FIG.  71. 


addendum  of  the  pinion,  and  the  root-circle  of  the  wheel  are  drawn 
in  the  usual  way,  and  the  addendum- circle  of  the  wheel  and  the 
root-circle  of  the  pinion,  as  in  the  exact  example.  These  drawn, 
apply  the  involute  table  as  for  spur-gears. 


CHAPTER  VIII. 

COLOR  WORK. 

TINTING. 

163.  Introductory. — Tinting  is  the  art  of  applying  colors  to 
drawings,  and  as  a  " touch  of  color"  added  to  most  things  enhances 
their  beauty,  so  does  the  art  of  tinting  assist  in  the  production  of 
handsome  drawings.     The  art  is  much  used  in  the  preparation 
of  drawings  for  catalogue  illustrations,  this  particular  kind  of 
work  being  a  trade  in  itself   and  known  as  "wash  drawing." 
The  art  of  tinting  is,  however,  of  some  importance  to  the  ordinary 
engineer-draughtsman,    being   much   used   by   the   architectural 
engineer  for  coloring  plans  and  perspectives  of  buildings,  and 
by  others  for  expediting  the  drawing  of  sections,  the  sectioned 
part  being  colored  as  a  substitute  for  cross-hatching. 

164.  Outfit. — The    outfit   needed   for  the   course   as   herein 
embodied  is  as  follows: 

(i).  Two  small  beakers  for  holding  water. 

(2).  Two  sable  or  camel's-hair  brushes,  or,  if  preferred,  one 
double-ended  brush,  one  end  for  color,  the  other  for  clear  water. 
The  brush  should  be  thick  in  the  body,  tapering  rapidly  to  a 
fine  point. 

(3).  A  nest  of  six  cabinet  saucers  in  which  to  mix  the  colors. 

(4).  A  bottle  of  library  paste  for  mounting  the  paper. 

(5).  A  small  hand  sponge  or  rag  with  which  to  sponge  the 
paper. 

(6).  A  six-inch  square  of  ordinary  fly-screening. 

(7).  A  tooth-brush  or  other  small,  stiff- bristled  brush. 

(8).  One-half  pan  (trade  term)  of  Chinese  white. 

(9).  A  small  stick  of  Chinese  or  India  black  ink. 

MS 


146  MECHANICAL  DRAWING. 

The  paper  best  adapted  for  tinting  differs  from  a  good  drawing- 
paper  in  that  it  is  comparatively  rough  of  surface. 

165.  Making  a  Stretch. — Since   the   tints   are   applied   in  a 
liquid  form,  there  is  more  or  less  of  a  tendency  for  the  paper  to 
"blister";  the  moisture  causing  it  to  stretch  and  the  corners  being 
fixed,  the  paper  blisters  in  proportion  to  the  amount  of  the  liquid 
applied.     To  meet  this  tendency,  the  paper  is  usually  "stretched" 
on  the  board.     This  is  done  as  follows: 

To  make  a  stretch,  first  select  the  surface  of  the  paper  to 
receive  the  drawing,  then  lay  the  paper,  with  this  side  up,  on 
a  drawing-board  and  "square"  the  top  edge  of  the  paper  with 
a  T-square;  next  slide  the  square  down  for  about  J"  and  turn 
up  this  i"  strip  of  paper  against  the  edge  of  the  T-square  blade; 
then  remove  the  square  and  fold  the  paper  back;  in  this  manner 
turn  up  and  fold  back  a  strip  of  about  J"  at  each  side  of  the  sheet, 
turning  the  top  side  first,  then  one  end,  then  the  other,  and  lastly 
the  bottom  side;  with  the  paper  thus  prepared,  turn  it  over  and 
with  a  'sponge  or  rag  apply  a  liberal  wash  of  clear  water,  being 
careful  to  keep  it  off  the  upturned  edges,  and  allow  it  to  soak 
for  two  or  three  minutes;  this  expands  the  paper  (should  a  very 
"tight"  stretch  be  desired,  the  paper  may  be  moistened  on  both 
sides;  for  the  exercises  of  this  course,  moistening  on  the  under- 
side will  suffice) ;  next  turn  the  paper  over  on  the  drawing-board, 
squaring  the  last  turned  edge  with  a  line  drawn  on  the  board, 
then  rub  the  paper  down;  the  moist  surface  will  adhere  to  the 
board  for  a  short  time;  now  apply  a  liberal  coating  of  paste  to 
the  turned-up  strips,  being  careful  to  keep  it  off  the  surface  to 
be  drawn  upon,  and  taking  them  in  the  reverse  order  as  turned 
up,  fold  them  back  and  rub  them  down  until  perfect  cohesion  is 
obtained;  when  the  paper  is  pasted  on,  and  while  the  paste  is 
yet  moist,  the  paper  should  be  drawn  taut  with  the  finger-tips; 
this  gives  an  additional  stretch  to  the  sheet,  which,  being  yet 
moist,  is  now  permitted  to  dry,  thus  contracting  the  expanded 
sheet,  and  the  pasted  parts  being  fixed,  the  paper  is  stretched. 

166.  Mixing  the  Colors. — To  mix  the  stick  ink,  rub  the  stick 
with  considerable  pressure  in  a  saucer  containing  a  small  quantity 


COLOR  WORK.  147 

of  water  until  the  desired  tint  is  obtained.  To  mix  the  Chinese 
white,  moisten  the  tip  of  the  cameFs-hair  brush  and  apply  it  to 
the  surface  of  the  color,  rubbing  briskly  and  turning  the  brush 
until  a  quantity  of  the  color  is  absorbed;  then  transfer  the  coloi 
to  a  saucer  containing  more  or  less  water,  according  to  the  quan- 
tity and  degree  of  color  wanted.  If  the  color  is  to  be  used  in 
the  ruling-pen,  the  pen  may  be  charged  directly  from  the  brush- 
tip. 

167.  Flat  Wash.— A  "flat  wash"  is  the  term  applied  to  the 
application  of  a  uniform  tint.  In  applying  the  color,  the  brush 
should  be  well  filled  and  a  small  "puddle"  of  color  made  on 
the  surface  to  be  colored;  this  puddle  is  washed  over  the  surface, 
then  picked  up  with  a  dry  brush.  This  applies  to  fairly  large 
surfaces;  if  the  surface  be  small,  the  brush  may  contain  but  little 
color  and  the  surface  be  "painted." 

The  tints,  if  permitted  to  stand  on  the  paper,  will  dry  in  a 
very  short  time,  especially  along  the  edges,  and  when  washed 
over  and  the  sheet  allowed  to  dry,  they  will  appear  streaked;  for 
this  reason  it  is  important  to  keep  all  parts  of  the  wash  moving — 
the  minimum  speed  is  quickly  ascertained  in  practice — until  the 
wash  is  finished.  If  one  cannot  work  with  sufficient  rapidity, 
the  drying  tendency  may  be  minimized  by  first  moistening  the 
surface  with  clear  water.  Such  a  procedure  is  advantageous 
also  as  a  vehicle  for  carrying  the  wash  into  intricate  parts  of 
the  drawing,  since  the  water  can  be  applied  slowly  and  with 
the  necessary  caution  to  preserve  the  lines;  however,  when  so 
doing,  care  must  be  exercised  to  produce  a  uniform  tint,  as  the 
added  water  will  tend  to  lighten  it. 

1 68.  Shading. — There  are  a  number  of  methods  for  shading 
with  tints,  principal  among  which  are  the  following: 

i.  To  shade  by  means  of  flat  tints,  lay  on  a  light  tint  flat 
wash  for  a  short  space,  then  soften  off  the  edge  with  a  clear, 
moist  brush-end;  when  dry,  begin  as  before,  and  this  time  carry 
the  wash  a  little  greater  distance,  then  soften  off  the  edge  as 
above;  in  this  manner  apply  a  number  of  coatings,  each  succes- 
sive one  covering  all  the  others — a  process  which  causes  the 


148  MECHANICAL  DRAWING. 

first  applied  wash  to  become  darkest  and  grades  from  it  to  the 
last  wash.  The  objection  to  this  method  is  the  great  amount  of 
time  consumed  in  its  application. 

2.  A  second  method  of  applying  shades  is  to  mix  the  color 
to  correspond  to  the  deepest  shade  and  make  a  puddle  of  this 
at  the  top  of  the  surface;   then  pick  up  a  quantity  of  clear  water 
with  the  brush  and  add  this  to  the  color  on  the  sheet,  washing 
it  down  for  a  short  distance;  then  add  more  water  and  wash  it 
down,  etc.,  adding  clear  water  each  time,  thus  thinning  the  tint 
and  grading  the  wash  from  dark  to  light.     This  method  requires 
much  practice  to  determine  the  exact  amount  of  water  for  a 
uniform  grading  of  the  tint. 

3.  A    third    method    is  to  begin  as   in  the  second  method, 
with  a  puddle  at  the  top,  but  this  time  thin  the  color  off  the 
sheet,  in  the  saucers,  then  apply  it.     In  these  two  methods  it  is 
important  that  a  fair- sized  puddle  be  maintained  on  the  paper, 
thus  insuring  a  more  even  thinning  of  the  color  and  a  uniform 
grading  of  the  tint.     Too  much  water  will  produce  a  streak,  too 
little  no  perceptible  change  of  tint. 

4.  In  this  method  first  wash  the  surface  to  be  shaded  with  a 
wash  of  clear  water;  do  not  apply  enough  water  to  cause  it  to 
stand  on  the  surface,  but  just  a  quantity  sufficient  to  cause  the 
paper  to  " glisten"  unifo  mly,  and  while  yet  wet  apply  the  color — 
which  should  be  quite  da  k — to  the  part  which  is  to  be  darkest  and 
draw  the  color  from  here  to  the  high  lights  by  streaking  the  sur- 
face with  bands  of  color  varying  in  width  and  spacing;  to  execute 
the  shade,  begin  at  the  high  light  with  a  clean,  moist  brush-tip, 
and  moving  the  brush  back  and  forth  at  right  angles  to  the  direc- 
tion of  advance,  work  through  the  bands  of  color  to  the  darkest 
part.      Should  the  shading  be  streaked  or  otherwise  irregular 
while  the  surface  is  yet  moist,  begin  again  at  the  high  light  with  a 
clean  brush  and  again  work  through  the  shade.    The  advantage 
of  the  method  is  that  as  long  as  the  surface  is  moist,  the  work 
may  be  gone  over  and  bettered. 

In  applying  the  bands-  of  color,  care  should  be  exercised  to 
have  just  the  right  quantity  of  the  liquid  in  the  brush-tip,  else 


COLOR   WORK.  149 

the  color  will  run;  if  too  much  is  applied,  or  if  too  little  is  added, 
the  shade  will  be  "pale."  The  color  should  be  quite  thick — 
heavy — and  the  brush  should  contain  that  quantity  which  remains 
after  wiping  the  brush-tip  a  few  times  on  the  edge  of  the  saucer. 

The  clean  brush  should  contain  a  quantity  of  water  remaining 
after  gently  squeezing  the  brush-tip  between  the  fingers — a  fairly 
"dry"  brush.  If  the  brush  contains  too  much  water,  the  tint 
will  be  thinned  too  much  and  the  shade  will  not  be  marked;  if 
there  be  too  little  water,  the  brush  will  pick  up  the  color  and 
the  shade  will  be  streaked. 

5.  When  the  surface  is  comparatively  small,  a  fifth  method 
may  be  used  to  advantage.  In  this,  apply  a  small  amount  of  the 
heavy  tint,  then  with  a  clean,  moist  brush  draw  the  color  out, 
and  as  it  is  carried  over  the  surface  it  will  become  thinned  and 
the  color  graded  from  the  original  dark  to  light.  The  exact 
amount  to  first  apply  is  a  matter  of  practice. 

To  minimize  a  tendency  to  dry  too  rapidly  in  the  first,  second, 
third,  and  fifth  methods,  clear  water  may  be  first  applied,  though 
the  surface  must  be  allowed  to  dry  to  a  point  where  the  "glisten" 
of  the  water  disappears  from  the  surface  of  the  paper,  else  the 
color  will  follow  the  water  and  cannot  be  controlled. 


STIPPLING.* 

169.  Introductory. — To  "stipple"  means  to  shade  by  means 
of  dots.  If  the  surface  to  be  stippled  is  small,  the  work  is  usually 
done  with  a  pen-point;  if  the  surface  is  of  some  size,  such  a  method 
is  too  time-consuming  and  difficult  where  good  results  are  desired. 
For  stippling  such  surfaces,  there  are  several  mechanical  methods 
which  may  be  used;  that  method  to  be  followed  in  this  course 
will  be  treated  of  as  being  typical  of  these  processes. 

If  a  piece  of  ordinary  wire  fly-screening  be  held  over  a  sheet 
of  paper  and  a  stiff  brush — such  as  a  tooth-brush — containing  a 
liquid  be  brushed  over  the  upper  surface,  it  will  throw  dots  of 

*  Also  called  "spatter  drawing." 


150  MECHANICAL   DRAWING. 

the  liquid  onto  the  paper.  This  simple  procedure  is  the  method 
to  be  followed  in  executing  the  exercises  in  stippling. 

170.  Method  of  Procedure.  —  For  good  results  the  paper 
should  be  stretched  as  for  tinting,  though  if  the  amount  of  sur- 
face to  be  stippled  is  small,  and  the  degree  of  shade  compara- 
tively light,  the  paper  may  be  secured  with  thumb-tacks  as  in 
ordinary  drawing.  The  color  is  mixed  as  for  tinting;  however, 
no  very  light  tints  are  used,  as  the  light  shade  is  here  produced 
in  a  different  manner.  The  figure  to  be  "  drawn"  is  executed 
on  a  sheet  of  fairly  stiff  paper — not  the  finished  sheet — and  is 
then  prepared  for  stippling  by  cutting  out  the  various  surfaces; 
that  is,  make  a  templet  for  the  figure,  then  lay  this  on  the  paper, 
matting  out  all  other  parts,  and  throw  the  dots  on  the  exposed 
area. 

To  stipple,  dip  the  brush  in  the  color,  shake  it  until  quite 
dry,  then  brush  it  across  the  screen.  If  the  brush  contains  too 
much  color  the  dots  will  not  be  clean-cut  and  often  will  run 
together  and  blur  and  blot. 

To  shade  lightly  and  uniformly,  hold  the  screen  some  dis- 
tance away — three  or  four  inches — from  the  paper;  as  the  screen 
is  moved  closer  to  the  paper  the  shading  may  yet  be  uniform, 
but  will  grow  darker.  Large  surfaces  are  stippled  by  moving  the 
screen  about,  and  shades  are  intensified  by  holding  the  screen  in 
one  place  and  close  to  the  paper. 


SKETCHING. 


PLATE  No.  12. 


pur&M   Uniwrstta 


PART  II. 

CHAPTER  IX. 
SKETCHING. 

171.  Introductory. — The  "course  in  mechanical  drawing"  as 
embodied  in  these  notes  is  divided  into  two  parts:  (i)  sketching, 
and  (2)  mechanical  drawing.     The  work  in  sketching  is  a  prelim- 
inary to  the  mechanical  execution  of  the  copies  given,  and  is 
intended   to    thoroughly  acquaint  the  student  with  the  funda- 
mentals of  mechanical  drawing. 

The  sketches  are  to  be  drawn  in  pencil,  on  a  specially' ruled 
paper,  with  the  aid  of  a  compass,  straight-edge,  and  scale. 

172.  Sheet  No.   i. — The  first  exercise,  Plate    No.   12,  is  an 
exercise  in  straight-lining  and  is  to  be  copied  free-hand,  exactly 
as  set  forth;  the  lettering  is  to  be  of  the  same  size  and  style  given, 
except  where  the  words  "Name"  and  "Date"  occur  the  student 
is  to  print  his  name  and  the  date  of  completing  the  sheet. 

The  paper  is  to  be  placed  as  for  writing,  and  with  the  hand 
in  the  natural  relative  position,  the  sheet  is  to  be  executed  without 
either  turning  the  paper  or  altering  the  position  of  the  body; 
great  care  should  be  taken  to  make  the  lines  of  uniform  weight 
and  as  straight  and  free  from  waves  as  possible. 

When  completed,  the  sheet  is  to  be  submitted  for  inspection 
and  acceptance  before  proceeding  with  the  next  exercise. 

173.  Sheet  No.  2.— Sheet  No.  2,  Plate  No.  13,  is  an  exercise 
for  the  training  of  the  eye  to  recognize  regular  curves  in  balance — 
symmetry;  it  is  a  free-hand  exercise  and  is  to  be  drawn  as  follows: 

Locate  the  center  lines  and  work  to  them  by  checking  the 

152 


PLATE  No.  13. 


SKETCHING. 


154  MECHANICAL  DRAWING. 

cross  lines  every  half  inch  or  less,  and  measure  the  distance  of 
the  points  at  which  the  curve  of  the  copy  crosses  these  cross  lines; 
then  lay  these  distances  off  (by  counting  spaces)  on  the  corre- 
sponding cross  line  of  the  drawing,  mark  the  points,  and  draw 
the  curve  through  these  points,  making  the  lines  very  light  until 
satisfactory;  then  trace  them  until  distinct. 

174.  Sheet  No.  3. — Sheet  No.  3  is  an  exercise  in  the  free-hand 
construction  of  letters  and  figures.     As  a  preliminary  for  this 
sheet,  Chapter  II  should  be  carefully  digested. 

To  draw  the  sheet,  use  Plate  No.  3  as  a  copy  and  construct 
the  following  alphabets: 

1.  Alphabet  No.  i,  making    the  letters  and  figures  J"  high. 
Note  the  copy  is  the  square  alphabet. 

2.  Draw  alphabet  No.  i,  J"  high. 

3.  Draw  alphabet  No.  3,  J"  high. 

4.  Draw  alphabet  No.  2,  the  guide-lines  to  be  \"  apart. 

5.  Draw  alphabet  No.  4,  the  guide-lines  to  be:  center  space  — 
J";  the  space  above  and  below  this  =  T\//. 

6.  Draw  a  number  of   miscellaneous  fractions  proportioned 
in  accordance  with  copy  No.  5. 

Reserve  a.  space  2"X  3"  in  the  lower  right-hand  corner  of 
the  sheet  for  the  following  title: 

SHEET  NO.  3. 
Letter-sheet  No.  I. 

Name.  Date. 

NOTE.— Begin  one  space  from  the  top  of  the  sheet  and  one 
space  in  from  the  left  border  line,  and  allow  one  space  between 
letters  and  two  spaces  between  rows. 

When  complete,  submit  the  sheet  for  inspection. 

175.  Sheet  No.  4. — Use  Plate  No.  3  as  a  copy  and  draw  two 
copies  of  No.  6 — entire  lower  half  of  the  plate;    the  student  is 
to  make  a  choice  of  size,  spacing,  and  balance  for  the  lettering,  and 
is  to  space  the  following  title  in  the  usual  letter  space : 


SKETCHING.  155 

SHEET  NO.  4. 
Letter-sheet  No.  2. 

Name.  Date. 

176.  Sheet  No.  5.— Sheet  No.  5,  Plate  No.  14,  is  a  mechanical 
drawing,  front  and  right  elevations  and  bottom  view,  of  a  lathe 
detail  (Fig.  70),  and  is  to  be  executed  exactly  like  the  copy,  using 
the  compass  and  straight-edge. 


THE  DETAIL 
FIG.   70. 

177.  Sheets  Nos.  6  to  20,  Inclusive. — These  sheets  are  to  be 
scale  drawings  from  models,  such  as  could  be  taken  into  a  shop, 
and  with  the  drawing  as  a  guide,  the  piece  could  be  produced. 

In  these  drawings  care  should  be  exercised  to  produce  a 
well-balanced  sheet,  to  place  the  views  so  as  to  bear  the  proper 
relation  to  one  another,  thus  rendering  the  sheet  easily  legible, 
and  to  give  all  necessary  dimensions  and  notes.  Reserve  the 
standard  letter  space — 2"X3" — for  a  title. 

To  illustrate  the  character  of  these  fifteen  drawings,  the  fol- 
lowing examples  are  given,  and  in  the  absence  of  models  from 
which  to  draw,  they  may  be  used  as  a  copy;  the  intention  of 
this  part  of  the  course,  however,  is  to  give  the  student  practice 


I56  MECHANICAL   DRAWING. 

PLATE  No.  14. 


FORM  D 


PAGE 


Purdue  University 


<-> 


UJ 


1,1 


SKETCHING.  .    157 

ill  original  drawing,  and  to  this  end  the  following  models,  which 
are  universally  obtainable,  are  named  as  being  representative: 

Hammers,  Bicycle  parts, 

Wrenches,  Stove  parts, 

Pipe-fittings,  Ink-bottles,  etc. 

Valves,  Spools, 

Machine  parts,  Boxes. 

The  notes  on  these  drawings  illustrate  a  common  shop  prac- 
tice, that  of  numbering  the  pattern  for  an  object,  so  that  should 
duplicates  of  the  piece  be  wanted  at  any  time,  in  place  of  supply- 
ing the  shop  with  a  new  drawing,  one  has  but  to  say  "Use  pattern 
No.  — ."  The  notes  as  to  the  number  wanted,  finish,  etc.,  are 
in  accordance  with  Sect.  51. 

The  name  of  the  piece  given  in  the  letter  space  represents 
real  practice ;  for  the  course  the  title  of  the  sheet  may  be  simply 
the  consecutive  "  SHEET  No.  — ." 

178.  Sheet  No.  21. — Draw  the  projections  of  a  2"  cube  with 
a  i"  square  hole  through  its  center,  and  assume  the  cube  to  rest  on 
the  horizontal  plane.     (Reference,  Sect.  75.) 

Use  Fig.  3,  Plate  No.  7,  as  a  copy,  with  the  following  dimen- 
sions: X  and  F  =  standard  sheet,  7"X9";  4  =  iJ",  £  =  2|", 
C=2j",  £>  =  2f",  E  =  i|",  F  =  iJ".  Execute  a  full-sized  draw- 
ing, drawing  the  figures  as  numbered.  Omit  all  dimension 
lines  and  letter  the  sheet  as  in  Fig.  21. 

179.  Sheet  No.  22. — Execute  a  full-sized  drawing  of  the  pro- 
jections of  a  blank,  hexagonal  nut,  Fig.  17,  the  nut  to  rest  on  the 
horizontal  plane.     (Reference,  Sect.  76.) 

Draw  the  figures  in  the  order  numbered,  using  the  following 
dimensions:  4  =  iJ",  £  =  ij",  C  (the  distance  of  the  center  line 
from  the  left  border)  =  2§ " ;  ground  line  to  be  in  center  of  sheet. 
Omit  all  dimensions. 

180.  Sheet  No.  23. — Execute  a  full-sized,  well-balanced  draw- 
ing of  Fig.  20,  completing  the  projection  B;   all  working  lines  to 
be  very  light  and  to.  show  on  the  finished  drawing.     Omit  all 
dimensions.     (Reference,  Sect.  77.) 


158 


MECHANICAL  DRAWING. 


PLATE  No.  15. 


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PLATE  No.  16. 


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160  MECHANICAL  DRAWING. 

PLATE  No.   17. 


SKETCHING. 


161 


PLATE  No.   1 8. 


162 


MECHANICAL   DRAWING. 


PLATE  No.  19. 


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SKETCHING. 


163 


PLATE  No.  20. 


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MECHANICAL   DRAWING. 


PLATE  No.  21. 


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PLATE  No.  22. 


i66 


MECHANICAL  DRAWING. 


PLATE  No.  23. 


SKETCHING. 


167 


PLATE  No.  24- 


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MECHANICAL  DRAWING. 


PLATE  No.  25. 


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1 70  MECHANICAL  DRAWING. 

181.  Sheet  No.  24. — Execute  a  full-sized  drawing  of  Fig.  21, 
drawing  the  figures  in  the  order  numbered;    show  all  working 
lines  and  omit  all  dimensions.     (Reference,  Sect.  78.) 

182.  Sheet  No.  25. — Execute    a  full-sized  drawing  of    Pro- 
jection No.  5,  Fig.  24.     (Reference,  Sect.  79.) 

183.  Sheet  No.  26,  Plate  No.  8.— A.    Execute    a    full-sized 
drawing  of  Fig.  5.     (Reference,  Sect.  80.) 

B.  Draw  the  developments  of  the  two  cylinders  (Fig.  4), 
the  sheet  to  be  well  balanced  and  all  working  lines  to  be  shown. 

184.  Sheet  No.  27,  Plate  No.  9.— A.    Execute    a    full-sized 
drawing  of  Fig.  5.     (Reference,  Sect.  81.) 

B.  Draw  the  developments  of  the -cylinder  and  of  the  cone. 
(Figs.  2  and  4.) 

185.  Sheet  No.  28. — A.  Execute  a  full-sized  drawing  of  Fig.  25. 
(Refe    nee,  Sect.  82.) 

B.  Draw  the  developments  of  the  cylinders,  cutting  cylinder  A 
along  the  element  4-4  and  cylinder  B  along  the  element  1-7  (out- 
side element). 

186.  Sheet  No.  29. — Execute  a  full-sized  drawing  of  Fig.  27, 
and  let  it  be  required  to  construct  a  shade  with  twelve  points 
around  the  bottom  as  indicated  by  the  dotted  lines;    allow  J" 
lap.     (Reference,  Sect.  83.) 

187.  Sheet  No.  30. — Execute  an  isometric  drawing  of  some 
simple  piece  of  mechanism,  drawing  from  the  model;    give  all 
dimensions  and  balance  the  drawing;    the  title  space  to  contain 
the  following: 

SHEET  NO.  30. 
Isometric  Drawing  No.  I. 
.     From  Model. 

Name.  Date. 

188.  Sheet  No.   31. — Execute  an  isometric  drawing  of  some 
simple  piece  of  mechanism,  drawing  from  the  mechanical  draw- 
ing of  the  object.     (Select  drawing  from  Sheets  Nos.  6  to  20, 
inclusive.)     Give  all  dimensions;    letter  as  above. 

189.  Sheet  No.  32. — Execute  an  original  isometric  drawing 


SKETCHING.  171 

in  accordance  with  either  Sheet  No.  30  or  31,  omit  all  dimensions, 
and  shade  the  drawing. 

190.  Sheet  No.  33. — Execute  an  original  assembled  mechan- 
ical drawing  of  some  fairly  simple  machine,  giving  all  dimen- 
sions and  notes  necessary  on  such  drawings.     (Read  Sect.  51.) 

191.  Sheets  Nos.  34  to  40,  Inclusive. — These  sheets  are  what 
will  be  known  as  "working-sketches."     They  are  to  be  free-hand, 
detail,  and  assembled  drawings,  drawn  from  the  various  machines 
in  the  different  laboratories,  and  are  later  to  be  reproduced  as 
pen-and-ink  scale  drawings;   some  of  them  to  be  on  paper  and 
others  to  be  drawn  on  tracing-cloth.     These  sketches  must  be 
complete,  not  with  reference  to  the  mere  drawing  alone,  but  with 
reference  to  dimensions,   notes,   etc.;    in  preparing  his  sketch, 
the  student  is  to  assume  he  is  never  again  to  see  the  object  and 
must  be  able,  months  hence,  to  construct  a  drawing  from  his 
sketch  such  that  the  thing  could  be  reproduced  with  the  draw- 
ing as  the  only  "guide." 


CHAPTER  X. 

THE  MECHANICAL  EXECUTION  OF  DRAWINGS. 

192.  Introductory. — Having  completed  the  course  in  sketch- 
ing, the  student  should  have  a  good  working  knowledge  of  the 
underlying  principles    of   mechanical  drawing  and  be  prepared 
to  take  up  the  study  of  drawing- tools  and  the  mechanical  con- 
struction of  practical  drawings.     With  this  end  in  view,  Plates 
Nos.  27  to  57,  inclusive,  are  given  as  examples  in  drawing,  calcu- 
lated to  further  the  student's  knowledge  of  the  subject,  to  be  his 
copy  for  the  manual  use  of  instruments,  and  being  representative 
sheets  of  every-day  practice,  to  afford  him  a  field  for  acquiring 
that  proficiency  of  execution  and  construction  which  is  required  of 
the  practical  draughtsman. 

In  the  execution  of  these  copies,  the  plates  are  to  be  accurately 
reproduced  in  accordance  with  the  instructions  given  for  each 
sheet,  and  with  such  dispatch  as  is  consistent  with  clean-cut, 
neatly  finished  work.  The  tools  required  for  the  work  are  such 
as  is  given  in  the  "Draughtsman's  Outfit,"  page  85. 

193,  Sheet   No.  i,  Plate    No.  27. — The  sheet  of  paper  given 
for  this  and  for  all  of  the  other  exercises  is  the  standard  9?"  X 12" 
sheet  and  is  to  finish  9^X1 2";  this  allows  a   waste  of  i"  to  be 
apportioned,  J"  at  the  top  and  \"  at  the  bottom  of  the  sheet  to  be 
used  as  "try"  paper(to  try  the  ruling-pen,  etc.,  on),  and  when  cut 
away   (when    the    sheet  is   completed)  removes   the   thumb-tack 
hole. 

To  secure  the  paper  to  the  drawing-board  (Fig.  53)  place  the 
paper  approximately  in  the  center  of  the  board — the  narrow 
way — and  3"  or  4"  nearer  the  left  side  of  the  board  (if  right- 
handed)  than  the  right  side;  now  place  the  T-square  on  the 

172 


MECHANICAL  EXECUTION  OF  DRAWINGS. 


175 


PLATE  No.  27. 


174  MECHANICAL  DRAWING. 

board  as  shown,  hold  the  paper  with  the  right  hand  and  with  the 
left  hand  on  the  T-square  head  move  the  square  towards  the  top 
of  the  board  until  the  top  edges  of  the  square  and  paper  coincide, 
turning  the  paper  as  is  necessary  to  "square"  it  with  the  square; 
with  the  paper  thus  "squared,"  remove  the  square  and  place  a 
thumb-tack  in  the  upper  left-hand  corner  of  the  sheet;  then  keep- 
ing the  paper  square,  run  one  hand — with  considerable  pressure 
— along  the  top  edge  of  the  paper,  stretching  ^it  to  the  right-hand 
corner,  and  tack  it;  these  two  corners  secured,  stretch  the  paper 
from  the  center  to  the  two  lower  corners  and  tack  them. 

The  paper  secured,  with  the  architect's  scale  lay  off  the 
8"Xn"  border  and  mark  the  cutting  lines;  now  with  the  T- 
square  for  horizontal  lines,  and  the  T-square  and  either  triangle 
for  vertical  lines,  draw  the  lines  through  these  points  which  form 
the  8"Xn"  inclosed  space  to  receive  the  drawing,  then  lay  out 
and  draw  the  2"X3"  letter  space. 

Working  to  the  dimensions  given,  lay  off  a  top  and  bottom 
line  for  the  row  of  lines  and  pencil  them  in,  making  all  of  the 
lines  light,  full  lines,  and  when  satisfactorily  spaced,  ink  them, 
showing  the  different  lines. 

For  the  second  row  of  figures,  locate  the  centers  for  the  circles, 
and  with  the  compass  set  with  the  proper  radius,  the  circles  may 
be  inked  without  any  preliminary  penciling. 

The  next  two  rows  are  to  be  penciled  in  as  dimensioned,  and 
then  inked  in  Much  care  is  necessary  here  to  produce  smooth 
lines  and  evenly  undulating  curves. 

The  bottom  row  on  the  plate  is  given  to  introduce  the  shade 
line — "back  lining"  drawings.  The  small  arrows  represent  the 
projection  of  the  rays  of  light,  which  are  assumed  to  be  parallel 
and  to  strike  the  plane  of  the  paper  at  an  angle  of  45°,  Con- 
sidering the  hollow,  rectangular  figure  on  the  left,  it  is  evident 
that  the  top  and  left-hand  lines  of  the  outside  of  the  figure  will 
be  in  the  light — illuminated — and  should  be  drawn  as  light  lines; 
also  that  the  bottom  and  right-hand  lines  of  the  outside  of  the 
figure  cut  off  the  light  and  represent  faces  of  the  object  which 
are  in  the  shadow,  and  should  be  drawn  as  heavy  or  shade  lines. 


MECHANICAL  EXECUTION  OF  DRAWINGS. 


175 


It  should  be  noted  that  the  shading  on  the  interior  of  the  draw- 
ing is  the  reverse  of  that  on  the  exterior. 

To  shade  the  circular  drawing  as  "called  for"  by  the  arrows, 
draw  the  diameter  E-F  with  the  45°  triangle,  then  draw  the 
diameter  G-H  at  90°  with  E-F  and  45°  with  A-B,  and  cutting 
E-F  at  a  point  about  ^V"  to  TV"  fr°m  tne  center;  now  with  the 
center  . defined  b;  the  intersection  of  A-B  and  C-D,  and  the 
proper  radius,  describe  the  circles,  and  to  shade  them,  take  a 
new  center — the  intersection  of  E-F  and  G-H — and  with  the 
same  radius  used  for  the  circles  (see  Fig.  71),  shade  the  larger 


FIG.   71. 

one  on  the  lower  right-hand  side  and  the  smaller  circle  on  the 
upper  left-hand  side. 

The  right-hand  figure  of  the  row  is  to  be  shaded  like  the 
copy. 

The  drawings  completed,  draw  top  and  bottom  guide-lines 
for  the  title  lettering,  the  top  row  to  be  J"  high,  the  middle  row, 
initial  letters  Ty  high,  other  letters  £"  high;  name  and  date, 
initial  letters  J"  high,  other  letters  •£$"  high ;  to  be  spaced  approxi- 
mately like  the  copy;  pencil  in  the  letters  until  satisfactory,  then 
ink  them  in  free-hand. 

When  completed,  submit  the  sheet  for  inspection  and  accept- 
ance before  taking  up  Sheet  No.  2. 


I76  MECHANICAL  DRAWING. 

194.  Sheet  No.  2,  Plate  No.  28. — This  is  an  exercise  for  a  test  in 
accuracy  of  manipulating  the  compass  and  bow-pen,  and  is  to  be 
first  constructed  in  pencil,  then  inked  in.     To  draw  the  sheet,  begin 
with  the  large  central  figure  by  locating  the  horizontal  and  vertical 
center  lines  intersecting  at  the  center  of  the  sheet;  with  this  point 
as  a  center  and  a  3"  radius,  describe  the  6"  circle;  then  with  the 
same  center,  describe  the  3"  circle,  and  with  the  points  in  which 
it  intersects  the  two  diameters  as  centers,  and  the  same  radius 
used  for  the  3"  circle,  draw  the  four  other  circles,  then  draw 
the  exterior  arcs  as  indicated. 

To  draw  the  three  small  designs,  locate  the  center  lines  and 
draw  the  2"  and  i3/16"  circles;  then  with  the  T-square  and  45° 
triangle  draw  the  two  diagonal  center  lines,  and  with  the  eight 
points  in  which  the  i3/16"  circle  intersects  the  four  center  lines  as 
centers  and  a  radius  of  iVie"  describe  the  eight  circular  arcs  as 
shown. 

195.  Sheet  No.  3,  Plate  No.  29. — This  sheet  is   given  as  an 
exercise  for  practice   in   ruling   straight   lines  and   to   acquaint 
the    student  with  the   standard    cross-hatchings    most  used  in 
drawing. 

To  draw  the  sheet,  pencil  in  the  fifteen  rectangles  as  per 
dimensions  and  proceed  as  follows:  For  cast  iron,  from  the 
upper  left-hand  corner  of  the  rectangle  draw  a  45°  line  to  the 
right  and  on  it  lay  off  points  Vie"  apart;  with  the  T-square  and 
45°  triangle  draw  the  ruling  through  these  points  and  when 
satisfactory,  ink  it  in,  inking  the  border  last;  this  applies  to  all  of 
the  fifteen  spaces,  i.e.,  ink  the  border  last. 

For  wrought  iron,  draw  a  45°  spacing  line  as  for  cast  iron,  lay 
off  3/32/'  lengths  and  draw  (in  ink)  the  light  line;  then,  using  the 
eye  for  the  spacing,  draw  a  heavy  line  about  1/32"  below  each 
light  line. 

For  steel,  use  the  eye  for  the  spacing  and  draw  two  fine  lines 
about  VM"  apart,  and  space  the  pairs  of  lines  about  Vie"  apart, 
inking  them  in  without  any  preliminary  penciling. 

For  brass  and  lead,  use  the  eye  for  the  spacing  (about  Vie") 
and  ink  directly. 


MECHANICAL  EXECUTION  OF  DRAWINGS. 


177 


PLATE  No.  28. 


lil 

UJ 

3: 
in 


58    I 


I?8  MECHANICAL  DRAWING. 

For  copper,  draw  the  pencil-lines  defining  the  blank  spaces 
and  ink  directly,  approximating  a  V16"  space  between  lines. 

Aluminum  and  wires  are  to  be  inked  directly,  with  approxi- 
mate spacings. 

Brick  and  stone  are  to  be  accurately  blocked  out  in  pencil, 
inked  in,  then  the  cross-hatching  approximated. 

Sand  is  made  free-hand  with  a  writing-pen,  dotted  in  in  ink 
directly. 

Earth  is  first  ruled  in  ink,  then  "touched  up,"  free-hand, 
with  a  writing-pen. 

Water  is  an  approximate  ruling,  and  glass  is  free-hand  pen 
work. 

The  spacing  given,  about  Y^",  applies  to  spaces  to  be  cross- 
hatched  of  about  the  size  of  the  rectangles  of  the  plate;  if  the 
space  to  be  cross-hatched  be  greater  than  this,  the  space  between 
lines  should  be  increased  proportionally;  if  smaller,  it  should  be 
decreased. 

196.  Sheet  No.  4,  Plate  No.  30. — This  is  to  be  a  free-hand 
exercise,  the  letters  to  be  "single-line"  letters.      To  draw  the 
sheet,  begin  with  the  upper-case  letters,  square  type,  and  draw 
the  top  and  bottom  guide-lines  and  pencil  in  the  alphabet,  omit- 
ting the  numbers  and  arrows  illustrating  the  number  and  direction 
of  the  strokes;   when  the  letters  are  properl    penciled,  ink  them 
in,  then  proceed  with  the  slanted  alphabet,  using  the  top  and 
bottom  guide-lines  and  inking  in  directly.     Complete  the  upper- 
case letters,  using  only  top  and  bottom  guide-lines  and  inking; 
directly. 

Execute  the  first  row  of  the  lower-case  letters,  first  in  pencil, 
omitting  arrows  and  numbers,  then  ink  them  in;  proceeding  as- 
for  the  upper-case  letters,  complete  the  alphabets. 

Put  on  the  headings  and  title  last,  then  erase  all  construction 
lines. 

Omit  all  dimensions. 

197.  Sheet  No.  5,  Plate  No.  31. — Fig.  i  is  an  elevation  draw- 
ing of  the  "business  end"  of  a  twist  drill  and  is  a  practical  exam- 
ple of  the  helix.    To  draw  the  figure,  locate  the  center  line, 


MECHANICAL   EXECUTION  OF  DRAWINGS. 


179 


PLATE  No.  29. 


I8o  MECHANICAL  DRAWING. 

describe  the  semicircle  1-2-3,  .  .  .  7  and  divide  it  into  six  equal 
arcs,  then  draw  the  rectangular  outline  and  copy  the  lines  of  the 
plate,  using  the  small  irregular  curve  as  is  suggested  by  the  dotted 
lines;  the  curve  at  the  top,  representing  a  broken  end,  is  drawn 
free-hand.  When  the  figure  is  accurately  drawn  in  pencil,  ink 
in  the  drawing  by  inking  the  curved  lines  first;  to  do  this,  use  the 
ruling-pen  and  curve,  holding  the  pen  in  a  vertical  position,  as 
shown  in  Fig.  72,  and  turning  the  pen  with  the  curve,  thus  keeping 
the  edges  of  the  nibs  parallel  at  all  points  with  the  guide. 


FIG.  72. 

Fig.  2  illustrates  two  methods  of  drawing  ellipses  when  the 
axes  are  at  right  angles.  First  method:  Locate  the  center  lines 
and  draw  the  two  circles;  divide  the  large  circle  into  twenty-four 
equal  parts  (this  can  be  done  by  means  of  the  T-square  and  both 
triangles)  and  draw  a  radial  line  to  each  point  of  division.  To 
locate  points  on  the  ellipse,  consider  the  radial  line  8-C;  from 
the  point  in  which  this  cuts  the  large  circle,  drop  the  perpen- 
dicular 8-4,  and  from  the  point  in  which  it  (8-C)  cuts  the  small 
circle,  draw  the  horizontal  8-8 — the  intersection  of  these  two 
lines  is  a  point  on  the  ellipse;  the  other  twenty- three  points  of 
the  curve  are  obtained  in  a  similar  manner.  The  points — the 
locus  of  the  curve — obtained,  use  the  irregular  curve  as  is  suggested 


MECHANICAL   EXECUTION  OF  DRAWINGS. 


181 


PLATE  No.  30. 


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1 32  MECHANICAL   DRAWING. 

by  the  plate  (note  the  lap  of  the  consecutive  positions)  and  pencil 
in  the  ellipse. 

Second  method:  Secure  a  strip  of  heavy  paper  one  edge  of 
which  is  a  straight  edge,  and  on  this  edge  lay  off  from  some  point, 
as  A,  a  length  A-C  equal  to  the  semi-major  axis  of  the  ellipse,  then 
from  the  same  point  (-4)  lay  off  a  second  length,  A-B,  equal  to 
B-C,  the  semi-minor  axis  of  the  ellipse;  now  with  the  point  C 
on  the  minor  axis  (extended)  and  the  point  B  on  the  major  axis 
rotate  the  strip  of  paper  (the  point  C  moving  back  and  forth  along 
the  minor  axis,  and  the  point  B  moving  up  and  down  along  the 
major  axis)  about  the  center,  C,  and  dot  the  travel  of  the  point  A ; 
the  curve  is  then  drawn  through  these  points. 

After  both  curve  5  have  been  accurately  constructed  in  pencil, 
trace  them  in  ink  with  the  ruling-pen  and  curve. 

Fig.  3.  This  figure  illustrates  a  method  of  constructing  any 
curve.  To  construct  the  curve,  locate  the  center  line,  draw 
horizontal  lines  every  J",  lay  off  on  these  the  lengths  given  in 
the  copy,  and  with  the  curve  pencil  in  the  drawing,  and  when 
satisfactory  ink  it  in. 

Fig.  4  illustrates  a  method  of  constructing  an  ellipse  when 
the  axes  are  not  at  right  angles.  To  construct  the  ellipse,  draw 
the  rhombus  A-B-C-D  and  the  major  (ii-n)  and  minor  (X-Y) 
axis  of  the  curve;  divide  the  semi-major  axis  (o-n)  into  a  num- 
ber of  equal  parts,  and  the  line  D-n  into  the  same  number  of 
equal  parts;  draw  radial  lines  from  point  X  through  the  points 
of  division  on  the  major  axis,  and  radial  lines  from  point  Y 
through  the  points  of  division  on  line  Z)-n;  the  intersections 
of  the  lines  drawn  to  the  same  numbered  point  are  the  points 
through  which  the  ellipse  is  drawn. 

The  plate  illustrates  the  locating  of  points  for  but  one-quarter 
of  the  curve;  points  for  the  other  three-quarters  are  located  in  a 
similar  manner. 

158.  Sheet  No.  6,  Plate  No.  32.— This  sheet  is  an  example 
of  structural  iron  draughting,  and  is  to  be  first  constructed  in 
pencil,  to  a  scale  of  i"  =  i',  without  any  letters  or  figures,  and 
submitted  for  inspection,  then  inked  in,  and  the  letters  and  figures 


MECHANICAL  EXECUTION  OF  DRAWINGS. 


183 


PLATE  No.  31. 


.184  MECHANICAL   DRAWING. 

drawn  last.     Space  the  lettering  of  the  title  so  as  to  add  the  line 


THE  STRUT 


FIG.  73 


199.  Sheet  No.  7,  Plate  No.  33. — This  sheet  is  given  to 
illustrate  methods  of  representing  screw-threads,  and  as  a  guide 
for  drawing  bolts  and  nuts.  Fig.  i  represents  a  hexagonal-headed 
bolt  and  nut;  to  draw  the  figure,  locate  the  center  line,  and  with 
dimension  D — the  diameter  of  the  bolt — equal  to  one  inch,  cal- 
culate all  other  dimensions  and  proceed  as  follows:  First  draw 
the  end  view,  circumscribing  the  hexagon  about  the  large  circle 
with  the  T-square  and  60°  triangle,  then  project  the  side  view  of 
the  nut  and  the  body  of  the  bolt.  To  draw  the  screw-threads, 
begin  on  the  right-hand  side  of  the  outline  of  the  bolt,  at  a  point 
as  dimensioned,  and  on  the  continuation  of  this  line  lay  off 
\"  divisions,  and  with  the  T-square  and  30°  triangle  draw  the 
V's  on  this  side;  now  on  the  left-hand  outline  of  the  bolt,  begin- 
ning at  a  point  2TV"  from  the  bolt- head — ry  nearer  than  on  the 
right  side — lay  off  a  number  of  J"  divisions,  and  draw  the  V's  on 
this  side;  to  end  the  bolt,  with  a  center  at  the  point  of  the  last 
V  (right  side)  and  a  radius  equal  to  the  diameter  of  the  bolt  (D), 
strike  an  arc  intersecting  the  center  line  (see  Fig.  2)  and  with  this 
point  as  a  new  center  and  the  same  radius,  strike  the  arc  of  the 
end  of  the  bolt ;  finish  by  connecting  the  tops  and  bottoms  of  each 
row  of  V's. 

The  drawing  represents  a  right-hand  V  thread,  an  outside 
thread  on  the  bolt,  and  an  inside  thread  in  the  upper  half  of  the 
nut;  note  the  direction  of  the  inclination  of  the  threads,  also 


MECHANICAL   EXECUTION  OF  DRAWINGS. 
PLATE  No.  32. 


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1 86  MECHANICAL   DRAWING. 

that  the  top  and  bottom  of  a  thread  are  directly  opposite  (on 
opposite  sides  of  the  bolt) ;  that  is,  the  nut  advances  one-half  thread 
in  traveling  half  way  around  the  bolt. 

The  pitch  of  a  thread  is  the  distance  from  the  point  of  one 
thread  to  the  point  of  the  next,  in  the  drawing,  shown  as  J",  and 
spoken  of  as  " eight  pitch."  The  figure  illustrates  a  convenient 
method  of  representing  all  V  threads,  though  not  always  a  true 
representation,  as  there  are  various  kinds  of  threads,  as  single, 
double,  triple,  etc.;  in  such  cases  a  note  relative  thereto  should 
be  added  to  the  drawing. 

In  addition  to  the  above,  there  are  a  number  of  types  of  threads, 
as  the  American  and  European  standard  forms  of  V  threads, 
square  threads,  buttress  threads,  and  others,  an  elaborate  expo- 
sition of  which  is  reserved  for  the  work  in  elementary  design; 
however,  the  simple  V  thread  as  given  is  conventional  for  all 
forms  of  V  threads,  unless,  of  course,  an  accurate  representation 
is  desired,  and  is  rendered  specific  by  the  addition  of  a  note, 
as  "U.  S.  standard  V,  double,  4  pitch." 

The  V  thread  is  always  drawn  showing  a  60°  V,  using  the 
T-square  and  60°  triangle. 

Fig.  2  represents  a  square-headed  bolt  and  nut,  showing  a 
left-hand  V  thread.  The  end  view  is  drawn  first  and  the  re- 
mainder of  the  figure  constructed  substantially  the  same  as  in 
Fig.  i. 

Fig.  3  represents  a  chamfered,  hexagonal-headed,  square- 
threaded  bolt.  To  draw  the  figure,  locate  the  center  line,  draw 
the  end  view  by  first  drawing  the  construction  circle  A-B-C  (this 
circle  does  not  appear  in  the  finished  drawing)  and  circumscribing 
the  hexagon  about  it,  then  project  the  head  of  the  bolt  and  pro- 
ceed with  the  thread,  which  is  analogous  with  the  V  thread. 

The  drawing  of  this  figure  is  to  be  shade- lined  in  accordance 
with  the  other  drawings  of  the  sheet;  the  " shade"  should  be 
drawn  outside  of  the  outline  dimensions. 

The  conventions  given  for  representing  screw-threads  are 
at  best  tedious  and  difficult,  especially  so  for  threads  of  small 
diameter.  To  further  expedite  the  work,  the  conventions  illus- 


MECHANICAL   EXECUTION  OF  DRAWINGS. 


187 


PLATE  No.  33. 


i88 


MECHANICAL  DRAWING. 


trated  in  Fig.  4  are  often  adopted,  the  end  A  representing  a 
V  thread,  and  the  end  B  a  square  thread,  the  inclination  of  the 
lines  being  slightly  out  of  a  right  angle  with  the  side  lines  and 
all  parallel. 

200.  Sheet  No.  8,  Plate  No.  34. — This   sheet  is  given  as  a 
guide  for  drawing  block- letters  and  as  an  exercise  in  free-hand 
lettering.      The    block-letters    are    drawn    with    instruments    in 
accordance  with  the  directions  given  on  the  sheet;   the  remainder 
of  the  plate  is  to  be  drawn  by  first  ruling  top  and  bottom  guide- 
lines in  pencil,  then  executing  the  lettering  free-hand  with  the 
writing-pen  without  any  preliminary  lettering  in  pencil.       The 
letters  are  to  be  of  the  following  dimensions:     Captions,  initial 
letter  to  be  Ty  high,  other  letters  J"  high;    descriptive  matter, 
initial  letters,   J"  high,  other  letters  •£$"  high;     space  between 
lines  J". 

In  the  free-hand  work  great  care  must  be  exercised  to  make 
the  letters  of  uniform  height  and  spacing,  the  words  compact,  and 
the  lines  of  uniform  weight.  No  guide  or  construction  lines  are 
to  show  on  the  finishecl  sheet. 

20 1.  Sheet  No.  9,  Plate  No.  35. — This  plate  is  a  working- 


THE  FRAME 

drawing  of  a  simple  blue-printing  frame  of  a  size  to  print  the 
standard  sheet  of  this  course;   i.e.,  9"Xi2". 


MECHANICAL  EXECUTION  OF  DRAWINGS. 


189 


PLATE  No.  34. 


I9°  MECHANICAL   DRAWING. 

To  draw  the  sheet,  locate  the  center  lines  of  the  front  view 
(the  large  rectangular  figure)  and  working  to  these,  copy  the 
drawing  and  when  complete  project  the  side  views. 

202.  Sheet  No.  10,  Plate  No.  36. — This  plate  is  given  in  the 
nature  of  a  problem  in  drawing,  illustrating  the  relation  of  the 
different  views  of  an  object;  the  "problem"  is  to  construct  a 
plan  drawing  of  the  object,  working  from  the  lines  and  dimen- 


THE  SUPPORT 
FIG.  75. 

sions  presented  by  the  two  elevations.  The  drawing  is  to  be  a 
scale  drawing,  one-half  size,  and  a  note  relative  thereto  inserted 
in  the  title  space. 

To  draw  the  sheet,  construct  the  drawing  on  the  right  hand — 
the  right  side  elevation — first,  then  project  the  front  elevation. 


MECHANICAL  EXECUTION  OF  DRAWINGS. 


191 


PLATE  No.  35. 


I92 


MECHANICAL  DRAWING. 


203.  Sheet  No.  n,  Plate  No.  37.— This  plate  presents  a 
working  drawing  of  a  locomotive -throttle  stuffing-box.  To  draw 
the  sheet,  locate  the  center  lines,  construct  the  front- elevation 


THE  BOX 
FIG.  76. 

drawing  first  (the  figure  on  the  left  of  the  plate),  then  project  the 
side  elevation. 

204.  Sheet  No.  12,  Plate  No.  38. — This  exercise  is  an  example 


Threaded  for  turnbuckle 


ONE  OF  THE  FORGINGS,  A  LATERAL  ROD 
FIG.  77 


of  bridge  drawing.     The  sheet  is  to  be  drawn  to  a  scale  of  i  J" 
(j-  size);    all  lettering  to  be  free-hand. 


MECHANICAL   EXECUTION  OF  DRAWINGS. 


193 


PLATE  No.  36. 


194  MECHANICAL  DRAWING. 

PLATE  No.  37. 


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MECHANICAL  EXECUTION  OF  DRAWINGS. 


195 


PLATE  No.  38. 


I96  MECHANICAL   DRAWING. 

205.  Sheet  No.  13,  Plate  No.  39. — This  sheet  is  a  drawing 
for  the  shop,  and  is  to  be  drawn  to  a  scale  of  3//  =  i/,  or  J  cir.e, 
and  a  "scale  note"  added  to  the  title  space. 


THE  HEAD 
FIG.  78. 

206.  Sheet  No.  14,  Plats  No.  40.  —  A  second  problem  in 
drawing,  similar  to  that  of  Sheet  No.  10,  is  here  introduced. 
Working  with  the  plan  and  elevation  drawings  and  to  center  lines, 


MECHANICAL  EXECUTION  OF  DRAWINGS.  197 

PLATE  No.  39. 


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I98  MECHANICAL   DRAWING. 

construct  a  right  end  view  drawing  of  the  stub,  to  a  scale  of 


In  addition  to  the  above  problem,  the  student  is  to  shade 
line — back  line — the  entire  sheet. 

207.  Sheet  No.  15,  Plate  No.  41. — This  sheet  is  a  detail  sheet, 
detailing  four  fittings  for  the  head  stock  of  a  wood- turning  lathe. 


Head-stock  Cap  Nut  for  Bearing^  One  of  the  Bearings 

LATHE  DETAILS' 
FIG.  80 

The  student— should  note  the  arrangement  and  balance  of  the 
sheet. 


MECHANICAL  EXECUTION  OF  DRAWINGS. 
PLATE  No.  40. 


199 


200  MECHANICAL   DRAWING. 

The  cross-hatched  portions  of  the  top  row  of  figures  illus- 
trate the  fit  of  the  bearings  and  the  use  of  the  pin  which  keeps 
them  (the  bearings)  from  turning. 

208.  Sheet  No.   16,  Plate  No.  42.— This  sheet  is  an  exercise 
in  free-hand  lettering.    The  student  is  to  decide  the  size  of  letters, 
spacings,  and  balance  of  the  sheet. 

209.  Sheet  No.  17,  Plate  No.  43. — An  assembled  shop  drawing 


THE  JOINT 
FIG.  81 

of  a  universal  joint.      Construct  a  full-size  drawing  and  shade 
the  end  view. 

210.  Sheet  No.   18,  Plate  No.  44. — This    sheet  introduces  a 
third  problem  in  drawing.    The  sheet  is  to  be  drawn  to  a  scale 
of  3"  =  i',  and  in  the  two  elevations  show  a  half  section  taken  on 
the  line  A-B-C  of  the  plan  drawing — the  plan  drawing  to  be 
drawn  like  the  copy. 

211.  Sheet  No.   19,  Plate  No.  45. — This  sheet  is  an  exercise 
for  practice  in  line  shading,  an  operation  for  which  the  following 
general  rules  may  be  found  useful: 

1.  A  surface  which  is  parallel  to  the  plane  of  projection  and 
in  the  light  is  uniformly  covered  with  light;  a  light  line  uniformly 
spaced  (i  and  2)  illustrates  the  ruling  for  such  a  surface. 

2.  A  surface  which  is  parallel  to  the  plane  of  projection  and 


MECHANICAL  EXECUTION  OF  DRAWINGS. 


201 


PLATE  No.  41. 


202 


MECHANICAL  DRAWING. 


PLATE  No.  42. 


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MECHANICAL   EXECUTION  OF  DRAWINGS. 
PLATE  No.  43. 


203 


204  MECHANICAL  DRAWING. 

PLATE  No.  44. 


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MECHANICAL   EXECUTION  OF  DRAWINGS. 


205 


PLATE  No.  45- 


206 


MECHANICAL   DRAWING. 


in  the  shadow  is  uniformly  dark    and  is  illustrated  by  uniform 
ruling  of  heavy  lines  closely  spaced. 


THE  BLOCK,  SECTIONED. 
FIG.  82. 


3.  Of  two  or  more  surfaces  which  are  parallel  to  the  plane 
of  projection,  the  surface  nearest  to  the  plane  is  the  lightest  and 
the  one  most  remote  the  darkest. 

4.  A  surface  which  is  inclined  to  the  plane  of  projection  and 
in  the  light  becomes  lighter  as  it  approaches. 

5.  A  surface  which  is  inclined  to  the  plane  of  projection  and 
in  the  shadow  is  dark  nearest  the  plane  and  becomes  lighter  as 
it  recedes. 

Figs,  i  and  2  show  a  uniform  line  uniformly  spaced;  3  and 
4  show  a  uniform  space,  variable  line,  drawn  from  light  to  heavy 
— "drawn  in";  5  and  6  show  the  same  "drawn  out." 

Figs.  7  to  12,  inclusive,  illustrate  conventional  shadings  for 
representing  cylindrical  surfaces;  7  and  8  show  a  uniform  line, 
variable  space;  9  a  uniform  space  and  variable  line,  and  Figs. 
10,  n,  and  12  variable  space  and  line. 

Fig.  13  is  a  uniform  line  uniformly  spaced,  used  to  represent 


MECHANICAL  EXECUTION  OF  DRAWINGS. 


207 


PLATE  No.  46. 


J 


208  MECHANICAL   DRAWING. 

flat  discs,  the  ends  of  cylinders,  etc.,  when  parallel  to  the  plane 
of  projection. 

Fig.  14  is  a  uniform  line  with  variable  spacing,  and  Fig.  15  a 
variable  space  and  line,  and  illustrate  conventions  for  represent- 
ing spheres. 

212.  Sheet  No.  20,  Plate  No.  46.— The  sheet  is  a  free-hand 
sheet;  the  student  is  to  decide  the  size  of  letter,  space,  balance 
etc.     ("  Schenectady    No.  2"  is   the   name   of   Purdue's  present 
experimental  locomotive.) 

213.  Sheet  No.  21,  Plate  No.  47. — Fig.  i  represents  a  sphere; 
Fig.  2  a  concave  surface,  the  interior  of  a  hollow  cylinder;   Fig.  3 
represents  one-half  of  a  hexagonal  prism;     Fig.  4  a  ring  which 
is  circular  in  section.     To  shade  the  view  on  the  left,  draw  a 
number  of   fine  lines  parallel  to  the  sides  and  "touch  up"  be- 
tween them,  free-hand,  with  an  etching-pen. 

Fig.  5  illustrates  two  shadings  for  screw-threads,  the  upper 
end  being  shaded  with  fine,  ruling-pen  lines  and  "touched 
up,"  free-hand;  the  lower  end  is  shaded  with  the  writing-pen 
alone. 

Figs.  6  and  7  represent  cylindrical  surfaces,  Fig.  6  illustrat- 
ing the  "treatment"  of  double-curved  surfaces  and  Fig.  7  the 
contrast  between  inside  and  outside  curves,  concave  and  convex 
surfaces,  respectively. 

Fig.  8  represents  a  number  of  flat  surfaces  parallel  with  the 
plane  of  projection,  as  an  elevation  of  a  flight  of  steps,  the  several 
heavy  lines  at  the  top  of  each  rise,  indicating  the  shadow  of  the 
nose  of  the  step  tread. 

214.  Sheet  No.  22,  Plate  No.  48. — This  sheet  is  given  as  a  pre- 
liminary to  the  drawing  of  gear- teeth,  and  is  also  an  excellent 
exercise   for   practice   in    the    use   of   the    irregular   curve;    the 
chapter  on  gearing  should  be  carefully  read  before  beginning  the 
drawing. 

The  sheet  is  to  be  a  full-size  drawing  to  the  dimensions 
given,  and  is  to  be  executed  in  accordance  with  Sect.  152.  All 
lines,  letters,  and  figures  of  the  copy  are  to  be  shown  on  the  fin- 
ished sheet;  omit  all  dimensions. 


MECHANICAL  EXECUTION  OF  DRAWINGS. 


209 


PLATE  No.  47. 


210  MECHANICAL  DRAWING. 

215.  Sheet  No.  23,  Plate  No.  49.— Here  is  presented  a  first 
exercise  in  the  construction  of  gear- teeth.     The  sheet  is  to  be  a 
full-size  drawing,  and  is  to  be  executed  in  accordance  with  Sect. 
1 60.     The  finished  sheet  is  to  show  all  lines,  letters,  and  figures, 
except  the  dimension  lines,  given  in  the  copy. 

216.  Sheet  No.  24,  Plate  No.  50. — This    sheet  is  a    second 
exercise  in  the  construction  of  gear-teeth,  and  is   to  be  drawn 
full  size,  in  accordance  with  Sect.  161 ;    the  finished  sheet  is  to 
appear  like  the  copy,  without  the  dimensions. 

217.  Sheet    No.    25,    Plate   No.    51.— The   sheet   is   another 
exercise  in  the  construction  of  gear- teeth,  and  is  to  be  a  full-size 
drawing,  to  be  executed  in  accordance  with  Sect.  162;   the  sheet 
is  to  be  finished  the  same  as  the  other  sheets  of  the  set. 

218.  Sheet  No.  26,  Plate  No.   52. — Here  we  have  presented 
a  practical  example  of  the  construction  of  gear-teeth,  the  drawing 
being  a  front  and  side  elevation  drawing  of  a  pair  of  involute 
gears.     The  sheet  is  to  be  a  full-size  drawing,  and  is  to  be  exe- 
cuted in  accordance  with  Sect.  160.     The  finished  sheet  is  to  show 
all  lines,  letters,  and  figures,  given  in  the  copy. 

219.  Sheet   No.    27,    Plate    No.    53. — Before    beginning    this 
sheet  the  student    should  read    Chapter  VIII.  on   color  work. 
.The  exercise  is  a  first  exercise  for  the  brush,  and  is  to  be  exe- 
cuted on  a  special  paper — different  from  that  used  for  the  pre- 
ceding sheets,  in  that  the  surface  is  not  so  highly  calendered.     A 
cold-pressed  paper  gives  the  best  results. 

The  paper  should  be  neatly  stretched  on  the  board  in  accord- 
ance with  Sect.  165;  the  ink  used  should  be  a  "wash  ink"  pre- 
pared by  rubbing  stick  ink  in  a  saucer  containing  a  small  quantity 
of  water. 

Directions  for  Drawing. — Lay  out  the  sheet,  according  to 
the  dimensions,  in  light  pencil,  being  careful  to  draw  only  the 
lines  necessary  to  block  out  the  rectangles;  do  not  draw  lines 
within  these  spaces  necessitating  an  erasure,  thus  bruising  the 
surface,  as  this  would  show  through  the  wash.  Begin  with  i 
and  wash  in  the  top  row  of  rectangles;  it  will  be  noticed  that  the 
shade  increases  in  depth;  this  is  accomplished  by,  after  each 


MECHANICAL  EXECUTION  OF  DRAWINGS. 


211 


PLATE  No.  48. 


p          N'         M  L'          K  J'          I'          H  G'          F'         E  0' 


TWE  EPICYCLOID  AND  HYPOCYCLOID 
r 


212 


MECHANICAL  DRAWING. 


PLATE  No.  49. 


MECHANICAL   EXECUTION  OF  DRAWINGS. 


213 


PLATE  No.  50. 


214 


MECHANICAL   DRAWING. 


PLATE  No.  51. 


MECHANICAL   EXECUTION  OF  DRAWINGS. 
PLATE  No.  52. 


2I5 


UJ 

LU 

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if) 


216  MECHANICAL   DRAWING. 

wash,  rubbing  the  stick  of  ink  in  the  saucer;    the  tint  should 
be  inspected  by  sample  on  scrap-paper  before  applying. 

The  shaded  row  is  washed  in  in  accordance  with  one  of  the 
methods  for  shading  given  in  Sect.  168.  It  should  be  noted 
that  y-^4  and  y-B  are  alike  and  are  the  light  washes  of  the  row, 
that  8-^4  and  8-B  are  alike  and  are  a  shade  deeper  than  7 -A 
and  j-B,  and  that  <)-A  and  g-B  are  alike  and  are  the  heavy  shade 
of  the  row. 

The  tinted  row  is  washed  in  by  first  laying  a  flat  wash  over  the 
entire  rectangle,  and  when  dry  applying  the  shade  as  above. 

In  the  flat  wash  (top  row)  let  the  paper  be  first  washed  with 
clear  water  for  one  or  two  spaces,  that  the  student  may  note  the 
effect;  the  remainder  of  the  sheet  may  be  washed  in  directly. 

In  executing  the  sheet,  exercise  great  care  in  preserving  the 
outline  of  the  rectangles;  should  the  color  run  outside,  the  edges 
may  be  straightened  with  a  knife-point  and  eraser,  a  procedure, 
however,  which  does  not  add  to  the  beauty  of  the  sheet  and  is 
to  be  avoided  if  possible. 

In  inking,  ink  only  the  border-line  of  the  sheet — not  the  borders 
of  the  rectangles — omit  all  dimensions,  and  finish  the  sheet  by 
lettering  the  title  and  name  only.  When  finished,  cut  the  paper 
from  the  board  with  a  J"  margin  outside  of  the  border-line  on 
all  sides. 

Place  the  sheet  number — SHEET  No.  27 — in  the  upper  right- 
hand  corner. 

220.  Sheet  No.  28,  Plate  No.  54. — This  sheet  is  a  wash  draw- 
ing of  plane  surfaces  which  are  parallel  with,  and  inclined  to, 
the  plane  of  projection,  and  of  concave  and  convex  single-curved 
surfaces. 

To  wash  Fig.  i,  begin  on  the  left  with  the  proper  tint  and 
draw  it  out  to  the  right,  washing  entirely  across  the  rectangle; 
do  not  attempt  to  define  the  center  edge.  When  dry,  begin  at 
the  center  with  the  proper  tint  and  draw  it  out  to  the  right.  For 
2,  flat  wash  the  parallel  face  and  when  dry  shade  the  inclined 
sides  as  shown.  For  3,  lay  on  a  light  wash  first,  then  treat  each 
face  in  order  according  to  the  degree  of  shade.  For  4,  beginning 


MECHANICAL  bXHCUTlON  Oh  DRAWINGS. 
PLATE  No.  53. 


217 


218  MECHANICAL  DRAWING. 

at  the  left,  draw  out  the  tint  to  the  right  and  entirely  across  the  rect- 
angle; when  dry,  begin  at  the  right  side  and  draw  the  tint  to 
the  left.  For  5,  flat  wash  the  flat  surfaces  first,  then  shade  as  in  4. 

The  next  row,  representing  end  views  of  the  figures  in  the 
top  row,  are  all  flat  washes.  For  6,  flat  wash  the  circular  draw- 
ing, also  the  rectangular  section,  first  cross-hatching  it  with  the 
ruling-pen  and  the  wash  ink.  The  shading  of  this  figure  may 
be  done  according  to  the  fourth  method  of  Sect.  168.  Fig.  7 
is  a  flat  wash  of  three  tints.  For  Fig.  8,  the  circular  drawing  is  a 
flat  wash  of  two  tints  and  the  rectangular  drawing  a  wash  similar 
to  the  rectangular  drawing  of  6. 

Directions  for  Drawing. — Lay  out  the  sheet,  according  to 
the  dimensions,  in  light  pencil;  wash  all  flat  surfaces  first,  then 
shade  as  directed  above.  In  inking,  ink  the  border  only,  and 
finish  the  sheet  by  lettering  the  title  and  name. 

Place  the  sheet  number  in  the  upper  right-hand  corner. 

221.  Sheet  No.  29,  Plate  No.  55.— This  sheet  illustrates 
certain  well-known  mechanical  details,  washed  in  as  for  cata- 
logue illustration,  and  introduces  the  application  of  Chinese- 
white  for  bringing  out  the  lines.  Fig.  i  represents  a  coil  spring, 
2  a  section  of  a  cylinder  disclosing  a  piston,  3  a  portion  of  a 
square- threaded  bolt,  and  4  a  hexagonal- headed  bolt  and  nut — 
5  and  6  are  end  views. 

To  shade  the  spring,  cross-hatch  the  sections  with  the  ruling- 
pen,  using  wash  ink,  then  flat  wash  them;  shade  the  front  of 
the  spring  first,  then  the  parts  showing  at  the  rear.  To  shade, 
wash  in  one  curvature  at  a  time,  i.e.,  consider  the  top  wire  ex- 
tending across  the  front  of  the  spring;  beginning  at  the  top,  lay 
on  a  stripe  of  the  tint  all  the  way  across,  then  draw  it  down  at 
once ;  when  the  surface  is  dry,  begin  at  the  bottom  line  and  draw 
up  at  once;  again  allow  the  surface  to  dry,  then  beginning  at  the 
left  hand  lay  on  the  wash  and  draw  it  to  the  right  at  once;  next, 
shade  the  right  end  in  a  similar  manner. 

The  cylinder  is  shaded  in  a  like  manner,  one  curvature  at  a  time. 
The  section  is  cross-hatched,  free-hand,  with  the  tip  of  the  brush, 
then  flat-washed. 


MECHANICAL   EXECUTION  OF  DRAWINGS. 
PLATE  No.  54. 


219 


220  MECHANICAL  DRAWING. 

The  thread  is  also  shaded  one  feature  at  a  time. 

To  shade  the  bolt  and  nut  wash  in  all  the  flat  surfaces,  then 
shade  as  above. 

The  white  lines  are  ruled  in  with  the  ruling- pen  and  Chinese- 
white  ink;  this  is  done  the  last  thing. 

Directions  for  Drawing. — Lay  out  the  figures  according  to 
the  dimensions,  wash  in  as  directed,  and  finish  the  sheet  by  letter- 
ing as  shown.  All  dimensions  are  to  be  omitted. 

Place  the  sheet  number  in  the  upper  right-hand  corner. 

222.  Sheet  No.  30,  Plate  No.  56. — This  sheet  is  a  first  exer- 
cise in  stippling — shading  with  dots.  The  plate  shows  a  plan 
and  elevation  of  a  hexagonal  prism,  a  hexagonal  pyramid,  a 
cone,  and  a  cylinder.  The  figures  are  first  drawn  in  outline  on 
a  duplicate  sheet;  that  is,  the  figures  are  laid  out  in  the  same 
arrangement  relative  to  one  another  and  to  the  border-line  as  they 
will  appear  on  the  stippled  sheet,  and  are  then  cut  out  as  follows : 

With  a  knife-point  cut  out  the  plan  of  the  prism,  cone,  and 
cylinder  (5,  7,  and  8).  The  first  and  last  are  flat  surfaces  and 
are  stippled  uniformly  by  placing  the  "stencil"  on  the  sheet, 
border  to  border,  and  the  dots  thrown  through  the  openings  as 
directed  in  Sect.  170.  To  shade  'the  plan  of  the  cone  (7),  mat 
out,  with  strips  of  paper,  all  of  the  exposed  surface  except  a 
small  sector  in  the  part  to  be  darkest;  stipple  this  about  as  for 
the  flat  surfaces,  drawing  the  shade  at  the  radii;  now  increase 
the  area  of  the  sector,  then  stipple  the  exposed  surface  lightly 
again — this  will  cause  the  first  shaded  portion  to  grow  darker. 
Continue  increasing  the  size  of  the  sector  in  this  manner  until 
the  entire  circle  is  exposed,  when  the  view  will  have  been  shaded. 

For  the  plan  of  the  pyramid  (6  ,  cut  through  the  stencil  on 
the  lines  representing  the  edges  and  part  way  through  on  the 
base-lines;  with  the  stencil  in  position,  fold  back  the  lower  right- 
hand  triangle  and  stipple  the  exposed  surface  rather  dark;  now 
fold  back  the  bottom  triangle — the  first  remains  open — and  shade 
the  exposed  area;  next  fold  back  the  upper  right-hand  triangle 
and  shade  the  exposed  surface;  proceed  in  this  manner,  taking 
the  faces  in  the  order  of  the  degree  of  shade  and  shade  the 


MECHANICAL   EXECUTION  OF  DRAWINGS. 


221 


PLATE  No. 


222  MECHANICAL  DRAWING. 

entire  exposed  area  each  time,  thus  causing  the  faces  to  grow 
darker  in  the  order  of  exposure. 

To  shade  the  top  row,  i,  2,  3,  and  4,  cut  out  the  side  faces  of 
the  prism  and  of  the  pyramid,  and  the  outlines  of  the  cone  and 
cylinder;  place  the  stencil  in  position  and  shade  the  exposed 
surfaces  according  to  the  copy,  care  being  taken  to  protect  each 
surface  after  stippling;  these  shaded,  cut  out  the  front  face  of 
i  and  2  and  stipple  the  exposed  areas. 

Directions  for  Drawing. — In  stippling,  it  is  important  that 
the  stencil  be  protected,  that  is,  when  stippling  an  area,  mat  out 
the  surface  of  the  stencil  immediately  about  the  opening  with 
scrap-paper,  thus  keeping  the  moisture  off  the  stencil,  which  if 
allowed  on  would  cause  it  to  blister.  It  is  also  important  that 
the  stencil  have  good  contact  with  the  paper  to  produce  clean- 
cut  lines;  good  results  are  obtained  by  laying  small  weights  about 
the  edges  of  the  opening. 

In  inking,  ink  the  border-line  only,  omit  all  dimensions,  and 
finish  the  sheet  by  lettering  it  as  shown. 

Place  the  sheet  number  in  the  upper  right-hand  corner. 

223.  Sheet  No.  31,  Plato  No.  57. — Here  is  depicted  for  "show" 
purposes  a  form  of  insulator  (i,  2,  and  3)  and  an  ornamental 
cap  (4,  5,  and  6).  The  figures  are  first  drawn  on  the  stencil- 
paper,  then  the  sheet  executed  in  the  following  order: 

Cut  out  i,  the  interior  of  2,  the  darkest  circle  of  3,  all  of  4,  the 
interior  of  5,  and  the  center  of  6;  place  the  stencil  on  the  sheet, 
border  to  border,  weight  the  i"  center  of  i  and  3  in  position,  and 
shade  the  exposed  areas  according  to  the  copy.  Next  cut  out 
the  section  of  2  and  5,  the  second  circle  of  3,  and  all  of  6,  then 
shade.  Now  cut  out  the  ends  of  2,  all  of  3,  and  the  double  curved 
part  of  5;  mat  out  with  scrap-paper  the  exposed  parts  already 
stippled,  then  shade;  lastly,  cut  out  the  groove  of  3  and  the 
single  curved  surface  of  5,  mat  out  exposed  parts,  and  shade 
according  to  the  copy. 

Directions  for  Drawing. — Ink  the  border-line  only,  omit  all 
dimensions,  and  finish  the  sheet  by  lettering  it  as  shown. 

Place  the  sheet  number  in  the  upper  right-hand  corner. 


MECHANICAL  EXECUTION  OF  DRAWINGS. 
PLATE  No.  56. 


224  MECHANICAL  DRAWING. 

PLATE  No.  57. 


MECHANICAL  EXECUTION  OF  DRAWINGS. 


225 


224.  Sheets  Nos.  32  to  36,  Inclusive. — These  are  to  be  pen-and- 
ink  scale  drawings  of  the  "working  sketches  "of  the  work  in  sketch- 
ing, constituting  what  will  be  termed  "shop  drawings" — draw- 
ings for  shop  purposes.    These  drawings  are  to  be  prepared  in 
pencil  on  paper,  and  then  traced  in  ink  on  tracing-cloth,  and 
later  reproduced   in   blue-print. 

Great  care  must  be  exercised  in  the  preparation  of  these 
drawings  to  make  them  clear  and  complete  in  every  detail,  giving 
all  necessary  dimensions,  notes,  etc. 

225.  Tables.  —  To    work    most    efficiently    a    draughtsman 
should  surround  himself  with  tabulated  statements  of  much-used 
information;    if  he  be  a  designer,  he  should  have  tables  of  the 
diameter,  circumference,  and  area  of  circles,  the  weight  per  cubic 
foot  of  the  various  metals,  dimensions  of  standard  parts,  etc. 
The  student  in  elementary  mechanical  drawing,  while  not  needing 
a  complement  of  such  information,  often  has  occasion  to  know 
the  dimensions  of  the  nut  and  number  of  threads  per  inch  for 
a  bolt  of  certain  diameter,  the  size  of  tap-drill,  etc.,  the  size  of 
steam-  and  gas-pipe,  with  the  corresponding  threading,  informa- 
tion for  drawing  gear- teeth,  etc.    The  following  tables  are  ap- 
pended for  reference  in  such  cases: 

STEAM-  AND  GAS-PIPE. 


Normal 
Size. 

Actual 
Inside 
Diameter. 

Actual 
Outside 
Diameter. 

Number  of 
Threads 
per  Inch 

.27 

.40 

27 

.36 

•54 

18 

.49 

.67 

18 

.62 

.84 

14 

.82 

1.05 

14 

I 

1.05 

1  .  31 

lit 

If 

1.38 

1.66 

II; 

I* 

1.61 

1.90 

Ili 

2 

2.07 

2-37 

lit 

2* 

2.47 

2.87 

8 

3 

3-07 

3-50 

8 

3i 

3-55 

4 

8 

4 

4-03 

4-5 

8 

4\ 

I 

4-51 

5 

8 

5 

5-04 

5-56 

8 

6 

6.06 

6.62 

8 

Taper  of  threads  J"  per  i'. 

226 


MECHANICAL  DRAWING. 


BOLTS  AND  NUTS. 


Diameter 
of  Screw. 

Threads 
per  Inch. 

Diameter 
at  Root  of 
Thread. 

Distance 
between 
Flats, 
Hexagonal 
or  Square. 

Diameter 
Across 
Corners, 
Hexagonal. 

Diagonal  of 
Square. 

Tap-drill. 

j 

t    ' 

20 

.185 

i 

87/64 

% 

xi6 

( 

/ 

ffi 

18 

.240 

/l6 

%> 

1 

1 

16 

.294 

% 

5V64 

3V32 

%> 

7A 

14 

•344 

25/32 

5%4 

J/i6 

2%4 

i 

f 

13 

.400 

1 

I 

i| 

1%2 

( 

4 

^6 

12 

•454 

3V82 

I* 

!%2 

i 

I 

II 

•507 

1^ 

I%2 

gl 

17/&2 

\ 

| 

IO 

.620 

l| 

ijfg 

i| 

I 

j 

r 

9 

•731 

I2V32 

2V32 

t 

8 

•837 

if 

I* 

2^6 

2%2 

7 

.940 

Il%b 

2%2 

2i 

8%2 

7 

.065 

2 

2^6 

22%2 

I%2 

6 

.160 

2% 

217/32 

3%2 

i/ie 

6 

.284 

2f 

2f 

3i 

I%2 

5* 

-389 

2% 

23^32 

at 

I13/32 

5    . 

.490 

3^6 

32%2 

xi 

2 

4* 

.712 

3* 

3l 

43^ 

if 

2* 
2* 

4 

.962 
2-175 

i 

4^6 

Si'2 

2^2 

2; 

[ 

4 

2.425 

4i 

42%2 

6 

2/ie 

3 

3| 

2.628 

4f 

5t 

6% 

2| 

3l 

2.878 

5 

5% 

7} 

22%2 

3 

1 

3i 

3.100 

sl 

6%4 

71 

3%2 

3 

r 

3 

3-3I7 

6% 

8^6 

3^32 

4 

3 

3-566 

6* 

7%2 

8% 

3J%2 

Angle   of  thread=6o°.     Thickness   of  nut=  diameter  of  bolt. 
head=  one-half  distance  between  flats. 


Thickness  of 


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Johnson's  Theory  and  Practice  of  Surveying Small  8vo,  4  oo 

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Elements  of  Sanitary  Engineering 8vo,  a  oo 

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Martens's  Handbook  on  Testing  Materials.     (Henning.)    a  vols. STO,  7  50 

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Elements  of  Analytical  Mechanics 8vo,  3  oo 

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Berg's  Buildings  and  Structures  of  American  Railroads 4to,  5  oo 

Brooks's  Handbook  of  Street  Railroad  Location i6mo .  morocco,  i  50 

Butts's  Civil  Engineer's  Field-book i6mo,  morocco,  a  50 

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Sheep,  5  SO 

Law  of  Contracts 8vo,  3  oo 

Winthrop's  Abridgment  of  Military  Law xamo,  a  50 

MANUFACTURES. 

Bornadou's  Smokeless  Powder — Ifitro-cellulose  and  Theory  of  the  Cellulose 

Molecule iamo,  a  50 

Bolland'g  Iron  Founder iamo,  a  5* 

"  The  Iron  Founder,"  Supplement iamo,  a  50 

Encyclopedia  of  Founding  and  Dictionary  of  Foundry  Terms  Used  in  the 

Practice  of  Moulding iamo,  3  oo 

Blstler's  Modern  High  Explosives 8vo,  4  oo 

Bffront's  Enzymes  and  their  Applications.     (Prescott. ) 8vo,  3  oo 

Fitzgerald's  Boston  Machinist x8mo,  x  oo 

Ford's  Boiler  Making  for  Boiler  Makers x8mo,  x  oo 

Bopkins's  Oil-chemists'  Handbook 8vo.  3  oo 

Keep's  Cast  Iron. STO,  a  5* 

Loach's  The  Inspection  and  Analysis  of  Food  with  Special  Reference  to  State 

Control.     (In  preparation.) 
Matthews's  The  Textile  Fibres,    (7n  preu.) 

Metcalf' s  Steel    A  Manual  for  Steel-users xamo,  a  oo 

Metcalfe's  Cost  of  Manufactures — And  the  Administration   of  Workshops, 

Public  and  Private 8vo,  5  oo 

Meyer's  Modern  Locomotive  Construction 4to,  xo  oo 

Morse's  Calculations  used  in  Cane-sugar  Factories. x6mo,  morocco,  i  50 

*  Reisig's  Guide  to  Piece-dyeing 8vo,  35  oo 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Smith's  Press-working  of  Metals 8vo,  3  oo 

Spalding's  Hydraulic  Cement xamo,  a  oo 

Spencer's  Handbook  for  Chemists  of  Beet-sugar  Houses x6mo,  morocco,  3  oo 

Handbook  tor  sugar  Manufacturers  and  their  Chemists.. .  i6mo,  morocco,    a  oo 
Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced.    (In 

press.) 

Thorston's  Manual  of  Steam-boilers,  their  Designs,  Construction  and  Opera- 
tion  8vo,    5  oo 

10 


•  Walke's  Lectures  on  Explosive! 8vo,  4  oo 

WMt'i  American  Foundry  Practice xamo,  a  50 

Moulder's  Text-book lamo.  a  5» 

Wiechmann's  Sugar  Analysis Small  8vo,  a  50 

Wolffs  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Woodbury's  Fire  Protection  of  Mills 8vo,  a  50 

Wood's  Rustless  Coatings:  Corrosion  and  Electrolysis  of  Iron  and  Steel. .  .8vo,  4  oo 

MATHEMATICS. 

Baker's  Elliptic  Functions 8vo,  i  30 

•  Bass's  Elements  of  Differential  Calculus xamo,  4  oo 

Briggs's  Elements  of  Plane  Analytic  Geometry iamo. 


Compton's  Manual  of  Logarithmic  Computations iamo, 

Daris's  Introduction  to  the  Logic  of  Algebra 8vo, 

•  Dickson's  College  Algebra Large  iamo, 

•  Answers  to  Dickson's  College  Algebra 8vo,  paper, 

•  Introduction  to  the  Theory  of  Algebraic  Equations   Large  iamo, 


5* 
50 
50 
35 
35 
75 


Hateted's  Elements  of  Geometry 8vo, 

Elementary  Synthetic  Geometry . . . ; 8vo. 

Rational  Geometry iamo, 

•  Johnson's  Three-place  Logarithmic  Tables:    Vest-pocket  size paper,  15 

100  copies  for  5  oo 

•  Mounted  on  heavy  cardboard.  8  X 10  inches.  as 

10  copies  for  a  oo 

Elementary  Treatise  on  the  Integral  Calculus Small  8vo,  i  50 

Curve  Tracing  in  Cartesian  Co-ordinates iamo.  i  oo 

Treatise  on  Ordinary  and  Partial  Differential  Equations Small  8vo,  3  50 

Theory  of  Errors  and  the  Method  of  Least  Squares iamo,  i  50 

•  Theoretical  Mechanics iamo,  3  oo 

Laplace's  Philosophical  Essay  on  Probabilities.     (Truscott  and  Emory.)  iamo,  a  oo 

•  Ludlow  and  Bass.     Elements  of  Trigonometry  and  Logarithmic  and  Other 

Tables 8vo,  3  oo 

Trigonometry  and  Tables  published  separately Each,  a  oo 

•  Ludlow's  Logarithmic  and  Trigonometric  Tables 8vo,  x  oo 

Maurer's  Technical  Mechanics. 8vo,  4  oo 

Merriman  and  Woodward's  Higher  Mathematics 8vo,  5  oo 

Merriman's  Method  of  Least  Squares 8vo,  a  OO 

Rice  and  Johnson's  Elementary  Treatise  on  the  Differential  Calculus .  Sm. ,  8vo,  3  oo 

Differential  and  Integral  Calculus,  a  vols.  in  one Small  8vo.  a  50 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish. 8vo,  3  oo 

Wood's  Elements  of  Co-ordinate  Geometry 8vo,  a  oo 

Trigonometry:  Analytical,  Plane,  and  Spherical iamo,  x  oo 

MECHANICAL  ENGIHEERING. 

MATERIALS  OF  ENGINEERING,  STEAM-ENGINES  AND  BOILERS. 

Bacon's  Forge  Practice xamo.  x  50 

Baldwin's  Steam  Heating  for  Buildings iamo,  a  50 

Barr's  Kinematics  of  Machinery 8vo,  a  50 

•  Bartlett's  Mechanical  Drawing 8vo,  3  oo 

"              "        Abridged  Ed. 8vo,  x  5* 

Benjamin's  Wrinkles  and  Recipes iamo,  a  oo 

Carpenter's  Experimental  Engineering 8vo,  6  oo 

Heating  and  Ventilating  Buildings 8vo,  4  oo 

Gary's  Smoke  Suppression  in  Plants  using  Bituminous  Coal.     (In  prep- 
aration.) 

Clerk's  Gas  and  Oil  Engine Small  8vo,  4  oo 

Coolidge's  Manual  of  Drawing 8vo,    paper,  x  oo 

11 


Coolidge  and  Freeman's  Elements  of  General  Drafting  for  Mechanical  En- 
gineers.    (In  press.) 

Cromwell's  Treatise  on  Toothed  Gearing izmo,  x  50 

Treatise  on  Belts  and  Pulleys '. : . . . .  izmo,  i  50 

Durley's  Kinematics  of  Machines Svo,  4  oo 

Fiather's  Dynamometers  and  the  Measurement  of  Power lamo,  3  oo 

Rope  Driving i2mo,  2  oo 

Gill's  Gas  and  Fuel  Analysis  for  Engineers = izmo,  i  25 

Hall's  Car  Lubrication i2mo,  i  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  2  30 

Button's  The  Gas  Engine Svo.  5  oo 

Jones's  Machine  Design: 

Part  I. — Kinematics  of  Machinery Svo,  i  50 

Part  II. — Form,  Strength,  and  Proportions  of  Parts Svo,  3  oo 

Kent's  Mechanical  Engineer's  Pocket-book x6mo,   morocco,  5  oo 

Kerr's  Power  and  Power  Transmission Sro,  2  oo 

Leonard's  Machine  Shops.  Tools,  and  Methods.     (In  press.) 

MacCord's  Kinematics;  or,  Practical  Mechanism Svo,  5  oo 

Mechanical  Drawing 4to,  4  oo 

Velocity  Diagrams Svo,  i  50 

Mahan's  Industrial  Drawing.    (Thompson.) Svo,  3  50 

Poole's  Calorific  Power  of  Fuels 8vo»  3  oo 

Reid's  Course  in  Mechanical  Drawing Svo.  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design . .  Svo,  3  oo 

Richards's  Compressed  Air I2mo,  x  50 

Robinson's  Principles  of  Mechanism.    Svo,  3  oo 

Schwamb  and  Merrill's  Elements  of  Mechanism.     (In  press.) 

Smith's  Press-working  of  Metals   Svo,  3  oo 

Thurston's  Treatise  on    Friction  and    Lost  Work   in   Machinery  and   Mill 

Work Svo,  3  oo 

Animal  as  a  Machine  and  Prime  Motor,  and  the  Laws  of  Energetics.  i2mo,  i  oo 

Warren's  Elements  of  Machine  Constructior  and  Drawing Svo,  7  50 

Weisbach's  Kinematics  and  the  Power  of  Transmission.      Herrmann — 

Klein.) Svo,  5  oo 

Machinery  of  Transmission  and  Governors.     (Herrmann — Klein.).  .Svo,  5  oo 

HydrauLcs  and  Hydraulic  Motors.     (Du  Bois.) Svo,  5  oo 

Wolff's  Windmill  as  a  Prime  Mover Svo,  3  oo 

Wood's  Turbines  Svo,  a  50 

MATERIALS  OP  ENGINEERING. 

Bovey's  Strength  of  Materials  and  Theory  of  Structures Svo,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering.     6th  Edition, 

Reset Svo,  7  50 

Church's  Mechanics  of  Engineering Svo,  6  oo 

Johnson'*  Materials  of  Construction Large  Svo,  6  oo 

Keep's  Cast  Iron Svo,  2  50 

Lanza's  Applied  Mechanics Svo,  7  50 

Martens's  Handbook  on  Testing  Materials.     (Henning  ) .Svo,  7  50 

Merriman's  Text-book  on  the  Mechanics  of  Materials Svo,  4  oo 

Strength  of  Materials I2mo,  i  oo 

Hetcalf's  Steel.    A  Manual  for  Steel-users i2mo,  a  oo 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish Svo,  3  oo 

Smith's  Materials  of  Machines 12010,  x  oo 

Thurston's  Materials  of  Engineering 3  vols ,  Svo,  8  oo 

Part  H.— Iron  and  Steel Svo,  3  So 

Part  in.— A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents Svo  a  50 

Text-book  of  the  Materials  of  Construction Svo,  5  oo 

12 


Wood's  Treatise  on  the  Resistance  of  Materials  and  an  Appendix  on  the 

Preservation  of  Timber 8vo,  a  oo 

Elements  of  Analytical  Mechanics 8vo,  3  oo 

Wood's  Rustless  Coatings:  Corrosion  and  Electrolysis  of  Iron  and  Steel..  .8vo,  4  oo 


STEAM-ENGINES  AND  BOILERS. 

Carnot's  Reflections  on  the  Motive  Power  of  Heat.     (Thunton.) lamo,  i  50 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book.  .  i6mo,  mor.,  5  oo 

Ford's  Boiler  Making  for  Boiler  Maker* i8mo.  i  oo 

GOSS'B  Locomotive  Sparks 8vo,  a  oo 

Hemrnway's  Indicator  Practice  and  Steam-eng  ne  Economy nmo,  a  oo 

Button'*  Mechanical  Engineering  of  Power  Plants 8vo,  5  oo 

Heat  and  Heat-engines 8vo,  5  oo 

Kent's  Steam-bo'ler  Economy 8vo,  4  oo 

Kneass's  Practice  and  Theory  of  the  Injector 8vo  i  50 

MacCord's  Slide-valves 8vo,  a  OO 

Meyer's  Modern  Locomotive  Construction 4to,  10  oo 

Peabody's  Manual  of  the  Steam-engine  Indicator lamo,  x  90 

Tables  of  the  Properties  of  Saturated  Steam  and  Other  Vapors 8vo,  i  oo 

Thermodynamics  of  the  Steam-engine  and  Other  Heat-engines 8vo,  5  oo 

Valve-gears  for  Steam-engines .W.vt 8vo.  a  50 

Peabody  and  Miller's  Steam-boilers 8vo,  4  oo 

Fray's  Twenty  Yean  with  the  Indicator Large  8vo,  a  50 

Pupln's  Thermodynamics  of  Reversible  Cycles  in  Gases  and  Saturated  Vapors. 

(Osterberg.) xamo,  x  as 

Reagan's  Locomotives :  Simple*  Compound,  ami  Electric. . ......  f , «. . .  tamo,  a  50 

Rontgen's  Principles  of  Thermodynamics.     ( Du  Bois. ) ,4 ,,,^r. . . . . .  8vo ,  5  oo 

Sinclair's  Locomotive  Engine  Running  and  Management iamo,  a  oo 

Smart's  Handbook  of  Engineering  Laboratory  Practice xamo,  a  50 

Snow's  Steam-boiler  Practice 8vo,  3  oo 

Spangler's  Valve  gears 8vo,  a  50 

Notes  on  Thermodynamics lamo,  x  oo 

Spangler,  Greene,  and  Marshall's  Elements  of  Steam-engineering 8vo,  3  oo 

Thurston's  Handy  Tables 8vo.  i    50 

Manual  of  the  Steam-engine a  vols.  8vo,  10  oo 

Part  I. — History,  Structucc,  and  Theory 8vo,  6  oo 

Part  II. — Design,  Construction,  and  Operation 8vo,  6  oo 

Handbook  of  Engine  and  Boiler  Trials,  and  the  Use  of  the  Indicator  and 

the  Prony  Brake. 8vo  5  oo 

Stationary  Steam-engines 8vo,  a  50 

Steam-boiler  Explosions  in  Theory  and  in  Practice xamo  x  so 

Manual  of  Steam-boiler* , Their  Designs,  Construction,  and  Operation. 8vo,  5  oo 

Weisbach's  Heat,  Steam,  and  Steam-engines.     ( Du  Bois.) 8vo,  5  oo 

Whitham's  Steam-engine  Design 8vo,  5  os> 

Wilson's  Treatise  on  Steam-boilers.     (Flather.) i6mo,  a  50 

Wood's  Thermodynamics  Heat  Motors,  and  Refrigerating  Machines. . .  .8vo,  4  oo 


MECHANICS    AND  MACHINERY. 

Barr's  Kinematics  of  Machinery 8vo,  a  SO 

Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Chase's  The  Art  of  Pattern-making xamo,  a  SO 

ChordaL — Extracts  from  Letters xamo,  a  oo 

•Church's  Mechanics  of  Engineering 8vo,  6  oo 

Notes  and  Examples  in  Mechanics 8vo,  a  oo 

13 


Compton's  First  Lessons  in  MeUl-workine lamo, 

Compton  and  De  Groodfs  The  Speed  Lathe iamo, 

Cromwell's  Treatise  on  Toothed  Gearing i2mo, 

Treatise  on  Belts  and  Pulleys ." iamo, 

Dana's  Text-book  of  Elementary  Mechanics  for  the  Use  of  Colleges  and 


Schools. 


1 2  mo, 


50 
So 
So 
50 

50 


Dingey's  Machinery  Pattern  Making lamo, 

Dredge's  Record  of  the  Transportation  Exhibits   Building  of  the  World's 

Columbian  Exposition  of  1893 4to,  half  morocco,    5  oo 

Du  Bois's  Elementary  Principles  of  Mechanics: 

VoL     I. — Kinematics 8vo,    3  50 

Vol.   H. — Statics 8vo,   4  oo 

Vol.  m.— Kinetics 8vo,    3  50 

Mechanics  of  Engineering.    VoL  I Small  4to,     7  50 

Vol.  II. Small  410,    10  oo 

Dudley's  Kinematics  of  Machines  8vo,    4  oo 

Fitzgerald's  Boston  Machinist i6mo,    i  oo 

Flather's  Dynamometers,  and  the  Measurement  of  Power xamo,   3  oo 

Rope  Driring xarno,   a  oo 

GOM'S  Locomotire  Sparks 8ro  a  oo 

Hall's  Car  Lubrication xamo,    x  oo 

Holly's  Art  of  Saw  Filing i8mo.       75 

•  Johnson's  Theoretical  Mechanic* 12  mo,   3  oo 

Statics  by  Graphic  and  Algebraic  Methods 8vo,    a  oo 

Jones's  Machine  Design: 

Part  I.— Kinematics  of  Machinery STO,    i  50 

Part  II.— Form,  Strength,  and  Proportions  of  Parts STO,    3  oo 

Ken's  Power  and  Power  Transmission 8vo,   a  oo 

Lanza's  Applied  Mechanics 8ro,   7  50 

Leonard  s  Machine  Shops,  Tools,  and  Methods.    (In  press.) 

MacCord's  Kinematics;  or.  Practical  Mechanism 8vo,   5  oo 

Velocity  Diagram* STO.    i  30 

Maurer's  Technical  Mechanics STO.  4  oo 

Merriman's  Text-book  on  the  Mechanics  of  Material* 8ro,   4  oo 

•  Michie's  Elements  of  Analytical  Mechanic* STO,   4  oo 

Reagan's  Locomotives:  Simple,  Compound,  and  Electric lamo,   a  50 

Reid's  Course  in  Mechanical  Drawing 8vo,    a  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design . .  STO,   3  oo 

Richards's  Compressed  Air lamo,    x  50 

Robinson's  Principles  of  Mechanism STO,   3  oo 

Ryan,  Norris,  and  Hoxie's  Electrical  Machinery.    Vol.  I STO,  a  5* 

Schwamb  and.  Merrill's  Elements  of  Mechanism.    (Inprets.) 

Sinclair's  Locomotive-engine  Running  and  Management xamo, 

Smith's  Press-working  of  Metals STO, 

Materials  of  Machines xamo, 

Spangler,  Greene,  and  Marshall's  Elements  of  Steam-engineering STO, 

Thurston's  Treatise  on  Friction  and  Lost  Work  in  Machinery  and  Mill 
Work STO, 

Animal  as  a  Machine  and  Prime  Motor,  and  the  Law*  of  Energetics .  xamo,       oo 

Warren's  Elements  of  Machine  Construction  and  Drawing STO,   7  50 

Weisbach's    Kinematics    and    the  Power  of    Transmission.    (Herrmann — 

Klein.) STO,   5  oo 

Machinery  of  Transmission  and  Governors.     (Herrmann — Klein.). STO,   5  oo 
Wood's  Elements  of  Analytical  Mechanics STO,   3  oo 

Principles  of  Elementary  Mechanics. . .  * xamo,    x  as 

Turbines STO,    a  50 

The  World's  Columbian  Exposition  of  1893 4to,    x  oo 

14 


00 
00 
00 

oo 


METALLURGY. 

Bgleston's  Metallurgy  of  Silrer,  Gold,  and  Mercury: 

VoL   I.— Silrer STO,  7  50 

VoL   H.— Gold  and  Mercury 8vo.  7  So 

••  Iles's  Lead-smelting.     (Postage  o  cents  additional.) lamo,  a  50 

Keep's  Cast  Iron 8ro,  a  50 

Kunhardt's  Practice  of  Ore  Dressing  in  Europe STO.  I  90 

Le Chatelier's High-temperature  Measurement*.  (Boudouard — Burgess.).  iamo,  3  oo 

Metcalf' s  Steel     A  Manual  for  Steel-users iamo.  a  oo 

Smith's  Materials  of  Machines lamo,  I  oo 

Thurston's  Materials  of  Engineering.     In  Three  Parts 8vo.  8  oo 

Part  II.— Iron  and  Steel STO,  3  So 

Part  III.— A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents STO,  a  50 

Dike's  Modern  Electrolytic  Copper  Refining STO,  3  oo 

MINERALOGY. 

Barringer's  Description  of  Minerals  of  Commercial  Value.    Oblong,  morocco,  a  so 

Boyd's  Resources  of  Southwest  Virginia STO.  3  oo 

Map  of  Southwest  Virginia. Pocket-book  form,  a  oo 

Brush's  Manual  of  DeterminatiTe  Mineralogy.    (Penfleld.) STO,  4  oo 

Chester's  Catalogue  of  Minerals STO,  paper,  i  oo 

Cloth,  i  as 

Dictionary  of  the  Names  of  Minerals 8ro,  3  so 

Dana's  System  of  Mineralogy Large  STO,  half  leather,  ia  so 

First  Appendix  to  Dana's  Hew  "System  of  Mineralogy." Large  STO.  i  oo 

Text-book  of  Mineralogy STO,  4  oo 

Minerals  and  How  to  Study  Them xamo,  i  90 

Catalogue  of  American  Localities  of  Mineral* Large  STO,  i  oo 

Manual  of  Mineralogy  and  Petrography tamo,  a  oo 

Bakle's  Mineral  Tables. STO,  i  is 

Bgleston's  Catalogue  of  Minerals  and  Synonyms STO,  a  50 

Hussak's  The  Determination  of  Rock-forming  Minerals.     (Smith.)  Small  STO.  a  oo 

Merrill's  Non-metallic  Minerals:  Their  Occurrence  and  Use*. STO,  4  oo 

•  Penfield's  Notes  on  DeterminatiTe  Mineralogy  and  Record  of  Mineral  Tests. 

STO,  paper,  o  90 
Roaenbusch's   Microscopical  Physiography   of   the   Rock-making   Minerals. 

(Iddings.) STO.  5  oo 

e  TUlman's  Text-book  of  Important  Minerals  and  Docks STO,  a  oo 

Williams's  Manual  of  Lithology STO,  3  oo 

^— •- ••••          MINING. 

Beard's  Ventilation  of  Mines lamo,  a  50 

Boyd's  Resources  of  Southwest  Virginia STO,  3  oo 

Map  of  Southwest  Virginia Pocket-book  form,  a  oo 

•  Drinker's  Tunneling,  Explosive  Compounds,  and  Rock  Drills. 

4to,  half  morocco,  as  oo 

Sinter's  Modern  High  Explosives „. STO,  4  oo 

Fowler's  Sewage  Works  Analyses iamo, 

Goodyear 's  Coal-mines  of  the  Western  Coast  of  the  United  States 12  mo, 

Ihlseng's  Manual  of  Mining STO, 


••  Iles's  Lead-smelting.    (Postage  oc.  additional.) iamo, 

Kunhardt's  Practice  of  Ore  Dressing  in  Europe STO, 

O'DriscolTs  Notes  on  the  Treatment  of  Gold  Ores STO, 

•  Walke's  Lectures  on  ExplosiTes STO, 

Wilson's  Cyanide  Processes iamo, 

Chlorination  Process xamo. 

Hydraulic  and  Placer  Mining samo. 

Treatise  on  Practical  and  Theoretical  Mine  Ventilation iamo 

15 


50 
So 
oo 
oo 
So 
50 


SANITARY  SCIENCE. 

Copeland's  Manual  of  Bacteriology.     (In  preparation.) 

Folwell's  Sewerage.     (Designing,  Construction  and  Maintenance.) 8vo,  3  oo 

Water-supply  Engineering 8vo,  4  oo 

Fuertes's  Water  and  Public  Health i amo,  x  50 

Water-filtration   Works ismo,  a  50 

Gerhard's  Guide  to  Sanitary  House-inspection i6mo,  i  oo 

Good  rich's  Economical  Disposal  of  Town's  Refuse Demy  8vo,  3  50 

Hazen's  Filtration  of  Public  Water-supplies 8vo,  3  oo 

Kiersted's  Sewage  Disposal zamo,  i  25 

Leach's  The  Inspection  and  Analysis  of  Food  with  Special  Reference  to  State 

Control.     (In  preparation.) 

Mason's   Water-supply.    (Considered   Principally   from   a   Sanitary   Stand- 
point.)   3d  Edition,  Rewritten 8vo,  4  oo 

Examination  of  Water.     (Chemical  and  Bacteriological.) lamo,  x  25 

Merriman's  Elements  of  Sanitary  Engineering     8vo,  •  oo 

Nichols's  Water-supply.     (Considered  Mainly  from  a  Chemical  and  Sanitary 

Standpoint.)     (1883.) 8vo,  2  50 

Ogden's  Sewer  Design iamo,  a  oo 

Prescott  and  Winslow's  Elements  of  Water  Bacteriology,  with  Special  Reference 

to  Sanitary  Water  Analysis. . . . .-.'..-...  v/.^uwrfis^  •:••••.•. I2mo?  J  *5 

*  Price's  Handbook  on  Sanitation I2mo,  i  50 

Richards's  Cost  of  Food.    A  Study  in  Dietaries 12010,  i  oo 

Cost  of  Living  as  Modified  by  Sanitary  Science i2mo,  z  oo 

Richards  and  Woodman's  Air,  Water,  and  Food  from  a  Sanitary  Stand- 
point  8vo,  a  oo 

*  Richards  and  Williams'*  The  Dietary  Computer 8vo,  z  50 

Rideal's  Sewage  and  Bacterial  Purification  of  Sewage 8  vo ,  3  50 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  oo 

Whipple's  Microscopy  of  Drinking-water 8vo,  3  50 

Woodhull's  Notes  and  Military  Hygiene z6mo,  z  50 

MISCELLANEOUS. 

Barker's  Deep-sea  Soundings 8vo,  a  oo 

Bmmoni's  Geological  Guide-book  of  the  Rocky  Mountain  Excursion  of  the 

International  Congress  of  Geologists Large  8vc  z  50 

Fen-el's  Popular  Treatise  on  the  Winds 8vo  4  oo 

Haines's  American  Railway  Management  zamo,,  50 

Mott's  Composition,  Digestibility ,  and  Nutritive  Value  of  Food.  Mounted  chart.  *  5 

Fallacy  of  the  Present  Theory  of  Sound z6mo  oo 

Ricketts's  History  of  Rensselaer  Polytechnic  Institute,  1824-1894.  Small  8vo,  oo 

Rotherham's  Emphasized  New  Testament Large  8vo,  oo 

Steel's  Treatise  on  the  Diseases  of  the  Dog 8vo,  50 

Totten's  Important  Question  in  Metrology 8vo  50 

The  World's  Columbian  Exposition  ot  1893 4to,  oo 

Von  Behring's  Suppression  of  Tuberculosis.     (Bolduan.)     (In  pret».) 
Worcester  and  Atkinson.    Small  Hospitals,  Establishment  and  Maintenance, 
and  Suggestions  for  Hospital  Architecture,  with  Plans  for  a  Small 

Hospital zamo,  i  as 

HEBREW  AND  CHALDEE   TEXT-BOOKS. 

Green's  Grammar  of  the  Hebrew  Language 8vo,  3  oo 

Elementary  Hebrew  Grammar zamo,  z  35 

Hebrew  Chrestomathy 8vo,  a  oo 

Gesenius's  Hebrew  and  Chaldee  Lexicon  to  the  Old  Testament  Scriptures. 

(Tregelles.) Small  4to,  half  morocco,  5  oo 

Letteris'i  Hebrew  Bible 8vo,  a  a 

16 


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THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
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UL  3  01987 


NOV  12  1915 

AUG  22  '"16 
AUG  3  1S18 
tIOYl9tt»    CBRCUUTION 


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2  3  1987 


AUG  10  1S26 


OCT  & 
AUG   19    1930 


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